# How do you evaluate 5\sqrt { 6} - 3\sqrt { 24} + \sqrt { 150}?

Mar 1, 2017

$4 \sqrt{6}$

#### Explanation:

$5 \sqrt{6} - 3 \sqrt{24} + \sqrt{150}$

Write down the factors within each square root sign.

$5 \sqrt{2 \cdot 3} - 3 \sqrt{2 \cdot 2 \cdot 2 \cdot 3} + \sqrt{5 \cdot 5 \cdot 2 \cdot 3}$

Remove the squares from the square root signs.

$5 \sqrt{2 \cdot 3} - \left(3 \times 2\right) \sqrt{2 \cdot 3} + 5 \sqrt{2 \cdot 3}$

Simplify.

$5 \sqrt{6} - 6 \sqrt{6} + 5 \sqrt{6}$

Keeping the square root separate, add or subtract the whole numbers according to their preceding signs.

$\left(5 - 6 + 5\right) \sqrt{6}$

$4 \sqrt{6}$