How do you simplify the square root of 275?

Jul 24, 2015

$275 = {5}^{2} \cdot 11$. Hence $\sqrt{275} = 5 \sqrt{11} .$
If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$
$\sqrt{275} = \sqrt{{5}^{2} \cdot 11} = \sqrt{{5}^{2}} \sqrt{11} = 5 \sqrt{11}$