# What is the square root of 90 - square root of 10?

Sep 8, 2015

Assuming we are dealing only with primary (positive) square roots:
sqrt(90)-sqrt(10) = 2sqrt(10

#### Explanation:

$\sqrt{90}$
$\textcolor{w h i t e}{\text{XX}} = \sqrt{{3}^{2} \times 10}$

$\textcolor{w h i t e}{\text{XX}} = \sqrt{{3}^{2}} \cdot \sqrt{10}$

$\textcolor{w h i t e}{\text{XX}} = 3 \sqrt{10}$

$\sqrt{90} - \sqrt{10}$

$\textcolor{w h i t e}{\text{XX}} = \left(3 \cdot \sqrt{10}\right) - \left(1 \cdot \sqrt{10}\right)$

$\textcolor{w h i t e}{\text{XX}} = 2 \cdot \sqrt{10}$

If we accept both positive and negative values for the square roots, possible solutions include:
$4 \sqrt{10} , - 2 \sqrt{10} , \mathmr{and} - 4 \sqrt{10}$