Question

question
express in simplest radical form.
√162

Explanation:

Step1: Prime - factorize 162

$162=2\times81 = 2\times9\times9$

Step2: Rewrite the square - root

$\sqrt{162}=\sqrt{2\times9\times9}$

Step3: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{2\times9\times9}=\sqrt{9\times9}\cdot\sqrt{2}$

Step4: Simplify $\sqrt{9\times9}$

$\sqrt{9\times9}=9$, so $\sqrt{162}=9\sqrt{2}$

Answer:

$9\sqrt{2}$