# Surds

Surds are numbers left in "square root form" (or "cube root form" etc).

**Addition and subtraction of surds**

a√b + c√b = (a + c)√b

a√b - c√b = (a - c)√b

**Examples**

4√7 - 2√7 = 2√7.

5√2 + 8√2 = 13√2

NB1: 5√2 + 3√3 cannot be manipulated because the surds are different (one is √2 and one is √3).

NB2: √a + √b is not the same as √(a + b) .

**Multiplication and Division**

√ab = √a × √b

√(a/b) = √a/√b

**Examples**

√5 × √15 = √75

= √25 × √3

= 5√3.

(1 + √3) × (2 - √8) [The brackets are expanded as usual]

= 2 - √8 + 2√3 - √24

= 2 - 2√2 + 2√3 - 2√6

A surd is the root of a whole number that has an irrational value.

Some examples are √2 √3 √10.

You can simplify a surd using the equation √ab = √a x √b and choosing a or b to be the square number.

You can find out more about surds here