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

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Answer 1 · 2014-10-30T17:07:14

By $\sqrt{75} = \sqrt{5^{2} \cdot 3} = \sqrt{5^{2}} \cdot \sqrt{3} = 5 \sqrt{3}$ $sqrt{75}=sqrt{5^2cdot3}=sqrt{5^2}cdot sqrt{3}=5sqrt{3}$ ,

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

Since $π \approx 3.14$ $pi approx 3.14$ ,

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

I hope that this was helpful.

Which number is larger between π15\frac{\pi}{15} and √3√75\frac{\sqrt{3}}{\sqrt{75}}?