### Surds

#### Rationalise the denominators of expressions of the form

• Simplify $$2\sqrt {7q} - \frac{{49\sqrt {2q} }}{{\sqrt {14} }}$$, where $$q > 0$$
• $$\begin{array}{1}2\sqrt {7q} - \frac{{49\sqrt {2q} }}{{\sqrt {14} }}\\ = 2\sqrt {7q} - \frac{{49\sqrt {2q} }}{{\sqrt {14} }} \times \frac{{\sqrt {14} }}{{\sqrt {14} }}\\ = 2\sqrt {7q} - \frac{{49\sqrt {28q} }}{{14}}\\ = 2\sqrt {7q} - \frac{{7 \times 2\sqrt {7q} }}{2}\\ = 2\sqrt {7q} - 7\sqrt {7q} \\ = \underline{\underline { - {\rm{ }}5\sqrt {7q} }} \end{array}$$