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Shaz
30/08/2025
Maths
SURDS full set of posters GCSE Maths
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30 Aug 2025
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GCSE Maths: How to Simplify Surds and More - Worksheets, Examples, and Answers
Shaz
@shaz2007
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Multiplying and Dividing Surds
This page focuses on multiplying and dividing surds in GCSE maths. It explains the rules for these operations and provides examples to illustrate the concepts.
When multiplying surds, multiply the numbers inside the roots and the numbers in front of the roots separately. For example:
Example: √3 × √14 = √ = √42 = √ = √2 × √21 = √2 × 3√7
The page also covers multiplication of surds involving brackets, such as 3 = 3√5 + 3√3.
For dividing surds, divide the numbers inside the roots and the numbers in front of the roots separately. For instance:
Example: √12 ÷ √3 = √ = √4 = 2
The page includes more complex examples and practice questions, which are crucial for understanding these concepts fully. Students can find additional multiplying and dividing surds worksheets with answers online for extra practice.
Highlight: When multiplying or dividing surds, always simplify the result if possible.
Rationalising the Denominator
This page explains the concept of rationalising the denominator in GCSE maths. It's an important technique for expressing fractions without surds in the denominator.
Definition: Rationalising the denominator is the process of eliminating surds from the denominator of a fraction.
The page provides step-by-step instructions for rationalising denominators with single terms and two terms. For a single term denominator:
- Multiply both numerator and denominator by the surd in the denominator.
- Simplify the resulting expression.
Example: Rationalise the denominator of 1/√3 Solution: × = √3/3
For denominators with two terms , multiply by the conjugate :
Example: Rationalise the denominator of 1/ Solution: ) × /) = / = 2 - √3
The page includes practice questions and examples of rationalising surds questions and answers. Students can find more resources like rationalising the denominator corbettmaths for additional practice.
Highlight: Rationalising the denominator is crucial for simplifying expressions and solving equations involving surds.
Simplifying Surds
This page covers the basics of simplifying surds in GCSE maths. It explains how to break down square roots into simpler forms and provides examples of simplifying various surd expressions. The page also introduces the concept of adding and subtracting surds.
Definition: Surds are irrational numbers that cannot be simplified to remove the square root.
To simplify surds, look for square numbers within the root. For example, √8 can be simplified to 2√2 because 8 = 4 × 2, and √4 = 2.
Example: Simplify √24 Solution: √24 = √ = √4 × √6 = 2√6
The page also covers how to simplify surds with a number in front, such as 3√150, which simplifies to 15√6.
Highlight: When adding or subtracting surds, the numbers inside the roots must be the same. For instance, 9√5 + 3√5 = 12√5.
Simplifying surds worksheets and practice questions are essential for mastering these concepts. Students can find additional resources like simplifying surds corbettmaths for further practice.
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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
GCSE Maths: How to Simplify Surds and More - Worksheets, Examples, and Answers
Shaz
@shaz2007
This guide provides a comprehensive overview of how to simplify surds in GCSE maths, covering simplification, multiplication, division, and rationalizing denominators. It offers detailed explanations, step-by-step examples, and key concepts to help students master surd operations.
• Simplifying surds... Show more
Multiplying and Dividing Surds
This page focuses on multiplying and dividing surds in GCSE maths. It explains the rules for these operations and provides examples to illustrate the concepts.
When multiplying surds, multiply the numbers inside the roots and the numbers in front of the roots separately. For example:
Example: √3 × √14 = √ = √42 = √ = √2 × √21 = √2 × 3√7
The page also covers multiplication of surds involving brackets, such as 3 = 3√5 + 3√3.
For dividing surds, divide the numbers inside the roots and the numbers in front of the roots separately. For instance:
Example: √12 ÷ √3 = √ = √4 = 2
The page includes more complex examples and practice questions, which are crucial for understanding these concepts fully. Students can find additional multiplying and dividing surds worksheets with answers online for extra practice.
Highlight: When multiplying or dividing surds, always simplify the result if possible.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Rationalising the Denominator
This page explains the concept of rationalising the denominator in GCSE maths. It's an important technique for expressing fractions without surds in the denominator.
Definition: Rationalising the denominator is the process of eliminating surds from the denominator of a fraction.
The page provides step-by-step instructions for rationalising denominators with single terms and two terms. For a single term denominator:
- Multiply both numerator and denominator by the surd in the denominator.
- Simplify the resulting expression.
Example: Rationalise the denominator of 1/√3 Solution: × = √3/3
For denominators with two terms , multiply by the conjugate :
Example: Rationalise the denominator of 1/ Solution: ) × /) = / = 2 - √3
The page includes practice questions and examples of rationalising surds questions and answers. Students can find more resources like rationalising the denominator corbettmaths for additional practice.
Highlight: Rationalising the denominator is crucial for simplifying expressions and solving equations involving surds.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Simplifying Surds
This page covers the basics of simplifying surds in GCSE maths. It explains how to break down square roots into simpler forms and provides examples of simplifying various surd expressions. The page also introduces the concept of adding and subtracting surds.
Definition: Surds are irrational numbers that cannot be simplified to remove the square root.
To simplify surds, look for square numbers within the root. For example, √8 can be simplified to 2√2 because 8 = 4 × 2, and √4 = 2.
Example: Simplify √24 Solution: √24 = √ = √4 × √6 = 2√6
The page also covers how to simplify surds with a number in front, such as 3√150, which simplifies to 15√6.
Highlight: When adding or subtracting surds, the numbers inside the roots must be the same. For instance, 9√5 + 3√5 = 12√5.
Simplifying surds worksheets and practice questions are essential for mastering these concepts. Students can find additional resources like simplifying surds corbettmaths for further practice.
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.
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
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 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