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