SurdsRevision Guide

By Flow Mathematics

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Higher

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AQA and OCR

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Contents

What are surds?

Simplifying surds by cancelling

Rule for simplifying surds

Expanding brackets with surds

Geometric surd sequences

Rationalising the denominator

Fractional indices and surds

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Grade7

What are surds?

Examples

Facts

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a) b)

c)

Surds can be added and subtracted. Surds can be simplified like algebra.

We can multiply and divide surdsby whole numbers.

Multiplying a surd by itself gives the integer itself.

1 2

3 4

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Grade7 Simplifying surds by cancelling

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Examples

a) b)

Answersa) b)

c)

Questions

c)

a) b)

c)

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Grade7 Rule for simplifying surds

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TipLook for factorsthat are square

numbers.

Example 1

Answer

Example 2

4 is a square numberthat goes into 24.

Answer 1 Answer 236 is the biggest square

number that goes into 72.We can simplify twice.

9 is a square number that goes into 72.

Questions

b)a) c)

d) e)

3√8 can be simplified

some more.4 is a square number that goes into 8.

TipYou can choosehow to simplify

fully.

We can't simplifyfurther. No

square numbersgo into 6.

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Grade7

Examples

Expanding brackets with surds

Click for answers 7

Answer

Answer

Answer

Answer

a)

b)

c)

d)

Question

The method isthe same aswith algebra.

a) b)

Multiply both partsinside the brackets

by √5.

Multiply both partsinside the second

bracket by √2 and then by 3.

The -2√7 and the2√7 cancel each

other out.

Cancel a √13from the topand bottom

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Grade7

The common ratio of this sequence is √2

Example

Answer

The nth term ofthis sequence is 2

Example

Geometric surd sequences

2 is the common

ratio.

8

n

NoteGeometric sequences

at GCSE have nthterms of the form r

where r is the common ratio.

n

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Summary

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Grade7

Click for answers+ more examples

Rationalising the denominator

Example 1

Answer

9

Answer

Example 2

Why?

Why?Questions

a) b) c)

Now thedenominator

is rational.

Change thesign in the

denominatorand multiply.

TipMultiply both

parts by3 + √2

This basicallymeans making

them wholenumbers.

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Grade7

Answer Answer

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Fractional indices and surds

Examples

Multiplicationindex law:

Add the powers

Fractional indexlaw.

Powers ofpowers law:

Multiply them!

Division index law: Subtractthe powers

a) b)

c)

Answer

d)

Answer

10

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