You need to know the following:[br][br][list][*]A square root such as[math]\sqrt{2}\text{ or }\sqrt{5}[/math] is a surd. (But not, eg.[math]\sqrt{4}=2[/math] )[/*][*]Surds multiply and divide as normal: [math]\sqrt{a}\times\sqrt{b}=\sqrt{ab}[/math] and [math]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}[/math][/*][*]Surds simplify by decomposing them into a product with a square number, and applying the root to that square - eg. [math]\sqrt{75}=\sqrt{25}\times\sqrt{3}=5\times\sqrt{3}=5\sqrt{3}[/math][/*][/list]

[list][*]You can [b]rationalise[/b] surds of the form [math]\frac{1}{\sqrt{2}}[/math] by multiplying by [math]\frac{\sqrt{2}}{\sqrt{2}}[/math] - this keeps the fraction the same value, but 'eliminates' the surd from the bottom: [math]\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}[/math][/*][/list]