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**Surds** are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. Surds are the root of numbers and not whole numbers.

Multiplication

Example:

√2 × √6 = √12 (= 2× 6)

= √4 × √3

= 2√3

Addition and Subtraction

4√3 - 2√3 = 2√3

5√5 + 8√5 = 13√5

Note: 5√7 + 3√3 cannot be manipulated because the surds are different (one is √7 and one is √3)

Example:

Simplify √12 + √27

12 = 3 × 4. So √12 = √(3 × 4) = √3 × √4 = 2 × √3.

Similarly, √27 = 3√3.

Hence √12 + √27 = 2√3 + 3√3 = 5√3