A comprehensive guide to working with surds in mathematics, covering... Show more
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Updated Mar 14, 2026
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Learn How to Simplify Surds and Add or Subtract Them Easily
L
Lilly Nolan
@lillynolan_kapb
1 / 6
Page 2: Adding and Subtracting Surds
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.
Page 3: Multiplying Surds
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.
Page 4: Worded Problems with Surds
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.
Page 5: Dividing Surds
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
Page 6: Rationalising the Denominator
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
Page 1: Simplifying Surds
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.
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Most popular content: Simplifying Radicals
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Students love us — and so will you.
4.6/5
App Store
4.7/5
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 Knowunity AI. 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 Knowunity AI. 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
Learn How to Simplify Surds and Add or Subtract Them Easily
L
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
Page 2: Adding and Subtracting Surds
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.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 3: Multiplying Surds
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.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 4: Worded Problems with Surds
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.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 5: Dividing Surds
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
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 6: Rationalising the Denominator
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
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 1: Simplifying Surds
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.
We thought you’d never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
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 Knowunity AI. 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 Knowunity AI. 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