# How do you add square root 3 + square root 12 - 4squareroot 75?

May 5, 2018

$- 17 \sqrt{3}$

#### Explanation:

$\sqrt{3} + \sqrt{12} - 4 \cdot \sqrt{75}$

$= \sqrt{3} + \sqrt{3 \cdot {2}^{2}} - 4 \cdot \sqrt{3 \cdot {5}^{2}}$

$= \sqrt{3} + 2 \sqrt{3} - 20 \cdot \sqrt{3}$

$= - 17 \cdot \sqrt{3}$

May 5, 2018

The answer will be $- 17 \sqrt{3}$, as shown by the calculation below.

#### Explanation:

$\sqrt{3} + \sqrt{12} - 4 \sqrt{75}$
=$\sqrt{3} + \sqrt{4 \cdot 3} - 4 \sqrt{25 \cdot 3}$
=$\sqrt{3} + \sqrt{4} \sqrt{3} - 4 \sqrt{25} \sqrt{3}$
=$\sqrt{3} + 2 \sqrt{3} - 4 \cdot 5 \sqrt{3}$
=$\left(1 + 2 - 20\right) \sqrt{3}$
=$- 17 \sqrt{3}$