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
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