A surd is a root that is irrational.

Examples of surds include √a, √2, 3√11, √a + √2, 3√15

Use the following rules to simplify surds:

√ab = √a x √b

√a/√b = √(a/b)

Remember that √a + b ≠ √a + √b

**Example**

Simplify the following as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

√108 - √12

**Answer**

Look for a low common factor of 108 and 12, which leaves square numbers when factorised. Here 3 is a common factor that leaves 36 and 4 respectively.

Thus:

108 = 36 x 3

12 = 4 x 3

√108 - √12

= √36 x 3 - √4 x 3

= √36 x √3 - √4 x √3

= 6 x √3 - 2 x √3

= (6 - 2) x √3

= **4√3**