# How do you simplify 2√3 + √2 - 4√3?

Sep 24, 2015

color(red)(2sqrt3 + sqrt2-4sqrt 3 = sqrt2 – 2sqrt3)

#### Explanation:

$2 \sqrt{3} + \sqrt{2} - 4 \sqrt{3}$

Start by combining the $\sqrt{3}$ terms.

$2 \sqrt{3} + \sqrt{2} - 4 \sqrt{3} = \sqrt{2} + 2 \sqrt{3} - 4 \sqrt{3}$

Factor $\sqrt{3}$ from the last two terms.

$\sqrt{2} + 2 \sqrt{3} - 4 \sqrt{3} = \sqrt{2} + \left(2 - 4\right) \sqrt{3}$

Combine the numbers inside the parentheses.

$\sqrt{2} + \left(2 - 4\right) \sqrt{3} = \sqrt{2} - 2 \sqrt{3}$

$2 \sqrt{3} + \sqrt{2} - 4 \sqrt{3} = \sqrt{2} - 2 \sqrt{3}$

That's about as simple as you can get it.