Question

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

Answer 1

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

`{sqrt{3}}/{sqrt{75}}=sqrt{3}/{5sqrt{3}}=1/5=3/15`.

Since `pi approx 3.14`,

`sqrt{3}/sqrt{75}=3/15 le pi/15`.

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I hope that this was helpful.