# How do you simplify: sqrt12+2sqrt27-5sqrt48 ?

Apr 6, 2017

$- 12 \sqrt{3}$

#### Explanation:

Let A$= \sqrt{12} + 2 \sqrt{27} - 5 \sqrt{48}$

When simplifying roots of integers it if often helpful to express the integer in terms of its prime factors.

$\sqrt{12} = \sqrt{2 \times 2 \times 3} = 2 \sqrt{3}$

$\sqrt{27} = \sqrt{3 \times 3 \times 3} = 3 \sqrt{3}$

$\sqrt{48} = \sqrt{2 \times 2 \times 2 \times 2 \times 3} = 2 \times 2 \sqrt{3}$

Hence A$= 2 \sqrt{3} + 2 \times 3 \sqrt{3} - 5 \times 4 \sqrt{3}$

$= 2 \sqrt{3} + 6 \sqrt{3} - 20 \sqrt{3}$

$= - 12 \sqrt{3}$