What is (3 sqrt5)/sqrt7?

Apr 1, 2018

The expression is equal to $\frac{3 \sqrt{35}}{7}$.

Explanation:

Rationalize the denominator by multiplying the top and bottom of the fraction by $\sqrt{7}$:

$\textcolor{w h i t e}{=} \frac{3 \sqrt{5}}{\sqrt{7}}$

$= \frac{3 \sqrt{5}}{\sqrt{7}} \textcolor{red}{\cdot \frac{\sqrt{7}}{\sqrt{7}}}$

$= \frac{3 \sqrt{5} \cdot \sqrt{7}}{\sqrt{7} \cdot \sqrt{7}}$

$= \frac{3 \sqrt{5} \cdot \sqrt{7}}{\sqrt{7}} ^ 2$

$= \frac{3 \sqrt{5} \cdot \sqrt{7}}{7}$

$= \frac{3 \sqrt{35}}{7}$

$\approx 2.53546 \ldots$