# Surds

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# Surds

A surd can be described as a root whose exact value cannot be found. It is an example of an irrational number; a number which cannot be expressed in the form:

In getting the value of a surd, the decimal number obtained is neither recurring nor terminating.
Consider:
√2, √3, √5, √6

## Simplification of Surds

Example 1
Simplify: √80

= √(16 x 5)
= √16 x √5
= 4√5

Example 2
Simplify: 3√2 + 4√2 - 5√2

= (3 + 4 - 5)√2
= 2√2

Example 3
Simplify: 5√8 - 2√2

= 5 x √4 x √2 - 2√
= 5 x 2 x √2 - 2√2
= 10√2 - 2√2
= (10 - 2)√2
= 8√2

## Rationalizing the Denominator

- Involves writing the denominator as a rational numbers.
Example 4
Rationalize the denominator