If the square root of three times a number is 15 how do you find the number?

Sep 16, 2015

If $\sqrt{3 n} = 15$
then $n = 75$

Explanation:

Method 1
$\sqrt{3 n} = \sqrt{3} \cdot \sqrt{n}$

$\sqrt{3} \cdot \sqrt{n} = 15$

$\sqrt{n} = \frac{15}{\sqrt{3}}$

$= \frac{15 \sqrt{3}}{3} = 5 \sqrt{3}$

$n = {\left(5 \sqrt{3}\right)}^{2}$

$= {5}^{2} \cdot {\left(\sqrt{3}\right)}^{2}$

$= 25 \cdot 3$

$= 75$

Method 2
If $\sqrt{3 n} = 15$

then

$3 n = {15}^{2} = 225$

$n = 75$