How do you simplify sqrt21/sqrt15?

Sep 9, 2016

$\sqrt{\frac{7}{5}} = \frac{\sqrt{35}}{5}$

It is debatable which one would be considered "simpler'

Explanation:

Two square roots being divided can be combined into one:

$\frac{\sqrt{21}}{\sqrt{15}} = \sqrt{\frac{21}{15}} \text{ } \leftarrow$ this can be simplified.

$\sqrt{\frac{21}{15}} = \sqrt{\frac{\cancel{3} \times 7}{\cancel{3} \times 5}}$

=$\sqrt{\frac{7}{5}}$

It is possible then to rationalise the denominator

$\sqrt{\frac{7}{5}} = \frac{\sqrt{7}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$

=$\frac{\sqrt{35}}{5}$