# Expressions Containing Square Roots

Notes on expressions containing square roots

- Created by: Natasha Naeem
- Created on: 10-06-11 13:56

First 178 words of the document:

Additional Mathematics

Algebra: Techniques

Section 3: Expressions involving square roots

Notes and Examples

These expressions can be treated in a similar way to algebraic ones i.e. by

collecting like terms and / or multiplying out brackets. They can be simplified

by using knowledge of square numbers and rationalised so that the

denominator of a fraction is always an integer rather than a square root term.

Remember that a a a

Example 1

Simplify if possible:

(i) 128 (ii) 75 48 (iii) 12 3

(iv) 2 3 3 3

(v) 1 2 1 2

Solutions

(i) 128 64 2 8 2

(ii) 75 48 25 3 16 3 5 34 3 3

(iii) 12 3 2 3 3 6

(iv) 2 3 3 3 6 3 3 2 3 3 3 3

(v) 1 2 1 2 1 2 2 2 1

Note with this last example that the product gives an

answer that does not contain a square root. It is just the

difference of two squares again.

You can see further examples on manipulating surds using the Flash resource

Working with surds and Rationalising the denominator.

You can test yourself using the interactive questions Adding and subtracting

surds, Multiplying surds and Rationalising the denominator.

© MEI, 24/07/09 1/1

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