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107
2
Hannah Murdoch
29/09/2025
Maths
Surds - National 5 Maths Revision
2,656
•
29 Sept 2025
•
National 5 Maths Surdsrevision guide provides essential information on... Show more
This page focuses on the important technique of rationalising the denominator when working with surds. This skill is crucial for National 5 Maths Surds past paper questions.
Definition: Rationalising the denominator means turning the surd at the bottom of a fraction into a whole number, while keeping the fraction the same.
The page explains that it's not possible to add or subtract surds with different surd signs. For example, √5 + √3 cannot be simplified further.
Highlight: Rationalising the denominator is important for various mathematical reasons and is a common requirement in National 5 Maths problems.
The method for rationalising the denominator is clearly explained: Multiply both the numerator and denominator by the surd in the denominator.
Three examples are provided to illustrate this process:
These examples demonstrate the step-by-step process of rationalising denominators with different types of surds, which is essential practice for National 5 Maths Surds revision worksheets.
Example: To rationalise 1/, multiply both numerator and denominator by √2: / = √2 / 6
This page provides valuable practice for students preparing for National 5 Maths exams, where rationalising denominators is a common topic in Surds questions.
This page introduces the concept of surds in National 5 Maths. Surds are square roots (or other roots) that do not have an exact answer. The page covers basic definitions, properties, and rules for working with surds.
Definition: A surd is a square root (or cube root, etc.) which does not have an exact answer.
Example: √2 = 1.414213... is a surd, while √25 = 5 is not a surd because it has an exact answer.
The page outlines important rules for working with surds:
Three detailed examples are provided to illustrate these concepts:
These examples demonstrate the step-by-step process of simplifying surds, which is crucial for National 5 Maths Surds revision.
Highlight: Understanding how to simplify surds is essential for solving more complex problems in National 5 Maths.
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.
App 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
National 5 Maths Surds revision guide provides essential information on simplifying and working with surds. This comprehensive resource covers key concepts, rules, and examples to help students master surds for their National 5 Maths exams.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on the important technique of rationalising the denominator when working with surds. This skill is crucial for National 5 Maths Surds past paper questions.
Definition: Rationalising the denominator means turning the surd at the bottom of a fraction into a whole number, while keeping the fraction the same.
The page explains that it's not possible to add or subtract surds with different surd signs. For example, √5 + √3 cannot be simplified further.
Highlight: Rationalising the denominator is important for various mathematical reasons and is a common requirement in National 5 Maths problems.
The method for rationalising the denominator is clearly explained: Multiply both the numerator and denominator by the surd in the denominator.
Three examples are provided to illustrate this process:
These examples demonstrate the step-by-step process of rationalising denominators with different types of surds, which is essential practice for National 5 Maths Surds revision worksheets.
Example: To rationalise 1/, multiply both numerator and denominator by √2: / = √2 / 6
This page provides valuable practice for students preparing for National 5 Maths exams, where rationalising denominators is a common topic in Surds questions.
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 concept of surds in National 5 Maths. Surds are square roots (or other roots) that do not have an exact answer. The page covers basic definitions, properties, and rules for working with surds.
Definition: A surd is a square root (or cube root, etc.) which does not have an exact answer.
Example: √2 = 1.414213... is a surd, while √25 = 5 is not a surd because it has an exact answer.
The page outlines important rules for working with surds:
Three detailed examples are provided to illustrate these concepts:
These examples demonstrate the step-by-step process of simplifying surds, which is crucial for National 5 Maths Surds revision.
Highlight: Understanding how to simplify surds is essential for solving more complex problems in National 5 Maths.
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.
107
Hol dir die App, um Zugang zu den smarten Tools mit interaktiven Karteikarten, Übungsaufgaben, Probeklausuren und Zusammenfassungen zu bekommen
Explore 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.
MathsThis comprehensive revision guide covers essential exponent properties, including basic, negative, and fractional powers. It features clear explanations and worked examples to help you simplify expressions and evaluate exponents effectively. Ideal for National 5 Maths students preparing for exams.
MathsExplore the concepts of surds, indices, and the distinction between rational and irrational numbers. This comprehensive guide includes methods for converting recurring decimals and rationalizing surds, tailored for GCSE Maths students. Enhance your understanding of rational exponents and the laws of indices with clear examples and explanations.
MathsExplore essential GCSE Maths concepts including quadratic equations, statistical measures, trigonometric functions, and volume formulas. This comprehensive summary covers topics like the quadratic formula, simultaneous equations, and graphing methods, providing students with a clear understanding of key mathematical principles. Ideal for exam preparation and revision.
MathsExplore key concepts in the Number section of the AQA GCSE Maths curriculum, including laws of indices, direct proportion, reverse percentages, and more. This comprehensive summary covers essential arithmetic operations, properties of exponents, and practical applications of percentage calculations. Ideal for exam preparation and understanding foundational mathematical principles.
MathsExplore the techniques for adding and subtracting surds with clear examples and practice questions. This summary covers simplifying radicals, rationalizing surds, and solving related problems, making it essential for mastering surd operations in mathematics.
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
