Question

question
express in simplest radical form.
\sqrt{162}

Explanation:

Step1: Factor the radicand

Factor 162 to find perfect square factors. We know that $162 = 81\times2$, and 81 is a perfect square since $9\times9 = 81$. So, $\sqrt{162}=\sqrt{81\times2}$.

Step2: Use the property of square roots

Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 81$ and $b = 2$), we get $\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}$.

Step3: Simplify the perfect square root

Since $\sqrt{81} = 9$, we substitute that in to get $9\times\sqrt{2}$, which is $9\sqrt{2}$.

Answer:

$9\sqrt{2}$