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Maths
14 Dec 2025
267
6 pages
Lilly Nolan @lillynolan_kapb
A comprehensive guide to working with surds in mathematics, covering simplification, operations, and rationalisation. This essential mathematical concept... Show more
The page explains the rules for combining like surds through addition and subtraction operations.
Highlight Only surds with the same number inside the root can be added or subtracted.
Example √80 + √125 can be simplified to 4√5 + 5√5 = 9√5
Definition Like surds are surds that have the same number under the root sign.
Vocabulary Terms - the parts of an expression separated by + or - signs.
This section covers the multiplication of surds and how to simplify the results.
Definition When multiplying surds, multiply the numbers outside the root signs together and the numbers inside the root signs together.
Example 3√2 × 5√12 = 15√24 = 30√6
Highlight Always simplify the final answer if possible by finding square factors.
The page demonstrates how to apply surd operations to solve real-world problems, particularly focusing on area calculations.
Example Finding the area of a triangle using surds Area = ½ × base × height
Highlight When expanding brackets containing surds, multiply each term carefully.
This section explains the process of dividing surds and rationalising denominators.
Definition To divide surds, divide the numbers outside the root signs and divide the numbers inside the root signs separately.
Highlight When dividing surds with two terms in the denominator, multiply both numerator and denominator by the conjugate of the denominator.
Example 16√24 ÷ 8 = 2√3
The final page focuses on the technique of rationalising denominators to eliminate surds from the bottom of fractions.
Definition Rationalising the denominator means eliminating any surds from the denominator of a fraction.
Highlight To rationalise a single surd denominator, multiply both numerator and denominator by the same surd.
Example √3/√2 becomes (√3 × √2)/(√2 × √2) = √6/2
This page introduces the fundamental concepts of simplifying surds through multiple examples. Students learn to break down numbers under square roots into their simplest form.
Definition A surd is an expression that contains an irrational root, typically a square root that cannot be simplified to a whole number.
Highlight Square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) are essential for simplifying surds.
Example √8 can be simplified to 2√2 by identifying the largest square factor (4) and writing √8 as √4 × √2.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the essential techniques for simplifying surds, including multiplication, division, and rationalizing denominators. This summary covers key concepts such as exponents, radical expressions, and step-by-step methods to express surds in their simplest form. Ideal for students looking to enhance their understanding of radical mathematics.
MathsExplore the fundamentals of Binomial Expansion, including Pascal's Triangle, Factorial Notation, and practical applications. This resource provides step-by-step solutions to binomial problems, estimation techniques, and calculator tips for computing binomial coefficients (nCr). Ideal for Year 1 A Level Maths students.
MathsExplore essential techniques for simplifying surds, including addition, subtraction, multiplication, and division. This guide covers rationalizing denominators and provides clear examples to enhance your understanding of surds and their properties.
MathsMaster the technique of rationalising surds with clear examples and step-by-step guidance. This summary covers essential methods for eliminating surds from denominators, making it ideal for students preparing for exams or seeking to strengthen their understanding of surds in mathematics.
MathsExplore the fundamentals of surds with this comprehensive summary. This resource covers key concepts, calculations, and examples to enhance your understanding of surds in mathematics. Ideal for students preparing for exams or seeking to strengthen their math skills.
MathsExplore the concept of surds, including their definition, examples, and methods for simplifying them. This summary covers key techniques for simplifying surds, such as identifying square factors and combining terms. Ideal for students looking to master radical expressions and enhance their understanding of square roots.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Lilly Nolan
@lillynolan_kapb
A comprehensive guide to working with surds in mathematics, covering simplification, operations, and rationalisation. This essential mathematical concept helps students understand how to manipulate expressions containing square roots effectively.
• Learn how to simplify surds in mathby breaking down... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The page explains the rules for combining like surds through addition and subtraction operations.
Highlight: Only surds with the same number inside the root can be added or subtracted.
Example: √80 + √125 can be simplified to 4√5 + 5√5 = 9√5
Definition: Like surds are surds that have the same number under the root sign.
Vocabulary: Terms - the parts of an expression separated by + or - signs.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section covers the multiplication of surds and how to simplify the results.
Definition: When multiplying surds, multiply the numbers outside the root signs together and the numbers inside the root signs together.
Example: 3√2 × 5√12 = 15√24 = 30√6
Highlight: Always simplify the final answer if possible by finding square factors.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The page demonstrates how to apply surd operations to solve real-world problems, particularly focusing on area calculations.
Example: Finding the area of a triangle using surds: Area = ½ × base × height
Highlight: When expanding brackets containing surds, multiply each term carefully.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section explains the process of dividing surds and rationalising denominators.
Definition: To divide surds, divide the numbers outside the root signs and divide the numbers inside the root signs separately.
Highlight: When dividing surds with two terms in the denominator, multiply both numerator and denominator by the conjugate of the denominator.
Example: 16√24 ÷ 8 = 2√3
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The final page focuses on the technique of rationalising denominators to eliminate surds from the bottom of fractions.
Definition: Rationalising the denominator means eliminating any surds from the denominator of a fraction.
Highlight: To rationalise a single surd denominator, multiply both numerator and denominator by the same surd.
Example: √3/√2 becomes (√3 × √2)/(√2 × √2) = √6/2
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the fundamental concepts of simplifying surds through multiple examples. Students learn to break down numbers under square roots into their simplest form.
Definition: A surd is an expression that contains an irrational root, typically a square root that cannot be simplified to a whole number.
Highlight: Square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) are essential for simplifying surds.
Example: √8 can be simplified to 2√2 by identifying the largest square factor (4) and writing √8 as √4 × √2.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the essential techniques for simplifying surds, including multiplication, division, and rationalizing denominators. This summary covers key concepts such as exponents, radical expressions, and step-by-step methods to express surds in their simplest form. Ideal for students looking to enhance their understanding of radical mathematics.
MathsExplore the fundamentals of Binomial Expansion, including Pascal's Triangle, Factorial Notation, and practical applications. This resource provides step-by-step solutions to binomial problems, estimation techniques, and calculator tips for computing binomial coefficients (nCr). Ideal for Year 1 A Level Maths students.
MathsExplore essential techniques for simplifying surds, including addition, subtraction, multiplication, and division. This guide covers rationalizing denominators and provides clear examples to enhance your understanding of surds and their properties.
MathsMaster the technique of rationalising surds with clear examples and step-by-step guidance. This summary covers essential methods for eliminating surds from denominators, making it ideal for students preparing for exams or seeking to strengthen their understanding of surds in mathematics.
MathsExplore the fundamentals of surds with this comprehensive summary. This resource covers key concepts, calculations, and examples to enhance your understanding of surds in mathematics. Ideal for students preparing for exams or seeking to strengthen their math skills.
MathsExplore the concept of surds, including their definition, examples, and methods for simplifying them. This summary covers key techniques for simplifying surds, such as identifying square factors and combining terms. Ideal for students looking to master radical expressions and enhance their understanding of square roots.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology