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185

15 Oct 2023

6 pages

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... Show more

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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√3 × √2/2×2√2 × √2 = √6/2

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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 1,4,9,16,25,36,49,64,81,100,121,1441, 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 44 and writing √8 as √4 × √2.



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

 

Maths

185

15 Oct 2023

6 pages

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

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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.

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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√3 × √2/2×2√2 × √2 = √6/2

Simplifying surds
(e.g.
●
D)
2)
Simplify the following
√8
√2 141
2√2
√24
√ √6
→
2√6
5) √240
√4 √60
A
2x√√√4x√√15
2×2×√15
4 15
4 is a
number

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

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 1,4,9,16,25,36,49,64,81,100,121,1441, 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 44 and writing √8 as √4 × √2.

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