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Surds

Learn How to Simplify Surds and Add or Subtract Them Easily

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Learn How to Simplify Surds and Add or Subtract Them Easily
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Lilly Nolan

@lillynolan_kapb

·

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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 math by breaking down square numbers and identifying perfect squares
• Master the adding and subtracting surds tutorial techniques with clear step-by-step examples
• Understand multiplication and division of surds through detailed explanations
• Follow the rationalising the denominator step-by-step guide to eliminate surds from denominators
• Practice with various worked examples and word problems to reinforce learning

15/10/2023

170

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

View

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

View

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

View

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

View

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

View

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

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

View

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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Subjects

/

Maths

/

Number

/

Surds

Learn How to Simplify Surds and Add or Subtract Them Easily

user profile picture

Lilly Nolan

@lillynolan_kapb

·

3 Followers

Follow

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 math by breaking down square numbers and identifying perfect squares
• Master the adding and subtracting surds tutorial techniques with clear step-by-step examples
• Understand multiplication and division of surds through detailed explanations
• Follow the rationalising the denominator step-by-step guide to eliminate surds from denominators
• Practice with various worked examples and word problems to reinforce learning

15/10/2023

170

 

10/11

 

Maths

5

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)/(√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, 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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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.