# Which number is larger between \frac{\pi}{15} and \frac{\sqrt{3}}{\sqrt{75}}?

##### 1 Answer
Oct 30, 2014

By $\sqrt{75} = \sqrt{{5}^{2} \cdot 3} = \sqrt{{5}^{2}} \cdot \sqrt{3} = 5 \sqrt{3}$,

$\frac{\sqrt{3}}{\sqrt{75}} = \frac{\sqrt{3}}{5 \sqrt{3}} = \frac{1}{5} = \frac{3}{15}$.

Since $\pi \approx 3.14$,

$\frac{\sqrt{3}}{\sqrt{75}} = \frac{3}{15} \le \frac{\pi}{15}$.

I hope that this was helpful.