Dividing surds

When dividing surds, we can divide the numbers outside the surds and the numbers inside the surds separately.

This can be written as:

\frac{a\sqrt{x}}{b\sqrt{y}}=\frac{a}{b}\sqrt{\frac{x}{y}}

Example: simplify \frac{6\sqrt{8}}{3\sqrt{2}}

• =\frac{6}{3}\sqrt{\frac{8}{2}}
• =2\sqrt{4}
• =2\times2
• =4

Example: simplify \frac{10\sqrt{18}}{5\sqrt{2}}

• =\frac{10}{5}\sqrt{\frac{18}{2}}
• =2\sqrt{9}
• =2\times3
• =6