Subjects
Biology
Chemistry
AP Chemistry
English
AP English Literature
Maths
Dec 7, 2025
462
2 pages
Leah Strawbridge @leahstrawbridge_kjnx
Surds are square roots that can't be simplified into whole numbers or fractions - they're really useful in... Show more
Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).
Take √2 or √5 - these are perfect examples of surds because they can't be simplified further. However, √81 might look like a surd at first glance, but it actually equals 9, so it's not a real surd.
The key to simplifying surds is hunting for square number factors. For example, with √20, you'd spot that 4 is a factor of 20 and 4 is a perfect square. This means √20 = √(4 × 5) = √4 × √5 = 2√5.
Quick Tip Always look for the largest square number that divides into your number - it'll save you time and effort!
Adding and subtracting surds follows a simple rule the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.
When the surds don't match initially, like √48 + √27, you'll need to simplify first. √48 becomes 4√3 and √27 becomes 3√3, giving you 4√3 + 3√3 = 7√3. Subtraction works exactly the same way 6√5 - 2√5 = 4√5.
Multiplying surds is actually quite straightforward. You can multiply the numbers under the square root signs together √2 × √98 = √196 = 14. When you have coefficients (numbers in front), multiply those separately 3√2 × 5√3 = 15√6.
Remember √a × √b = √(a × b) - this rule will be your best friend in surd calculations!
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
13
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the concepts of surds, expanding brackets, and rationalizing denominators in this comprehensive study resource. Ideal for Edexcel Maths GCSE students, this summary covers essential techniques and examples to enhance your understanding of radical expressions and algebraic manipulation.
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.
MathsThis comprehensive guide focuses on simplifying surds, rationalizing denominators, and working with radical expressions. It includes clear examples and step-by-step methods tailored for National 5 Maths (GCSE) students. Perfect for revision and enhancing your understanding of surds.
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 essential concepts of surds, including simplification, addition, subtraction, and rationalization of denominators. This comprehensive guide covers key rules and examples to enhance your understanding of square roots and radicals, tailored for GCSE Edexcel students.
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Leah Strawbridge
@leahstrawbridge_kjnx
Surds are square roots that can't be simplified into whole numbers or fractions - they're really useful in maths when you need exact answers rather than decimals. Don't worry, they're not as scary as they look, and once you get... Show more
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).
Take √2 or √5 - these are perfect examples of surds because they can't be simplified further. However, √81 might look like a surd at first glance, but it actually equals 9, so it's not a real surd.
The key to simplifying surds is hunting for square number factors. For example, with √20, you'd spot that 4 is a factor of 20 and 4 is a perfect square. This means √20 = √(4 × 5) = √4 × √5 = 2√5.
Quick Tip: Always look for the largest square number that divides into your number - it'll save you time and effort!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Adding and subtracting surds follows a simple rule: the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.
When the surds don't match initially, like √48 + √27, you'll need to simplify first. √48 becomes 4√3 and √27 becomes 3√3, giving you 4√3 + 3√3 = 7√3. Subtraction works exactly the same way: 6√5 - 2√5 = 4√5.
Multiplying surds is actually quite straightforward. You can multiply the numbers under the square root signs together: √2 × √98 = √196 = 14. When you have coefficients (numbers in front), multiply those separately: 3√2 × 5√3 = 15√6.
Remember: √a × √b = √(a × b) - this rule will be your best friend in surd calculations!
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
13
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the concepts of surds, expanding brackets, and rationalizing denominators in this comprehensive study resource. Ideal for Edexcel Maths GCSE students, this summary covers essential techniques and examples to enhance your understanding of radical expressions and algebraic manipulation.
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.
MathsThis comprehensive guide focuses on simplifying surds, rationalizing denominators, and working with radical expressions. It includes clear examples and step-by-step methods tailored for National 5 Maths (GCSE) students. Perfect for revision and enhancing your understanding of surds.
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 essential concepts of surds, including simplification, addition, subtraction, and rationalization of denominators. This comprehensive guide covers key rules and examples to enhance your understanding of square roots and radicals, tailored for GCSE Edexcel students.
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
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