Question

simplifying non - perfect square roots. use a calculator to make sure your answer evaluates to the same number as √180. check

Explanation:

Step1: Prime - factorize 180

$180=2\times2\times3\times3\times 5$

Step2: Apply square - root property

$\sqrt{180}=\sqrt{2^{2}\times3^{2}\times5}$

Step3: Simplify the square - root

$\sqrt{2^{2}\times3^{2}\times5}=\sqrt{2^{2}}\times\sqrt{3^{2}}\times\sqrt{5}=2\times3\times\sqrt{5}=6\sqrt{5}$

Answer:

$6\sqrt{5}$