# How do you simplify sqrt(88)?

Mar 17, 2018

$2 \sqrt{22}$

#### Explanation:

Find the prime factors of 88:
$88 = 2 \cdot 44 = 2 \cdot 2 \cdot 22 = 2 \cdot 2 \cdot 2 \cdot 11$

so $\sqrt{88} = \sqrt{2 \cdot 2 \cdot 2 \cdot 11}$
=$\sqrt{2 \cdot 2} \cdot \sqrt{2 \cdot 11}$
=$2 \cdot \sqrt{22}$
=$2 \sqrt{22}$

So to simplify a root, you break it down into its prime factors and extract any square numbers.