What is the square root of 225 minus the square root of 15 plus the square root of 60?

Nov 3, 2015

$\sqrt{225} - \sqrt{15} + \sqrt{60} = 15 + \sqrt{15} \approx 18.8729833462$

Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

Hence:

$\sqrt{225} - \sqrt{15} + \sqrt{60}$

$= \sqrt{{15}^{2}} - \sqrt{15} + \sqrt{{2}^{2} \cdot 15}$

$= 15 - \sqrt{15} + 2 \sqrt{15}$

$= 15 + \sqrt{15}$