# What is the square root of (5) multiplied by (7+ square root of 10)?

Sep 15, 2015

$7 \sqrt{5}$ + $5 \sqrt{2}$

#### Explanation:

It is $\sqrt{5} \times \left(7 + \sqrt{10}\right)$

Multiply them

$\sqrt{5} \times 7 + \sqrt{5} \times \sqrt{10} = 7 \sqrt{5} + \sqrt{50}$

You know that $\sqrt{50}$ can be simplified as

$\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{{5}^{2} \cdot 2} = 5 \cdot \sqrt{2}$

$\sqrt{5} \cdot \left(7 + \sqrt{10}\right) = 7 \sqrt{5} + 5 \sqrt{2}$