# How do you simplify 3sqrt(-48)?

Dec 20, 2015

$12 i \sqrt{3}$

or more proper form

 0 + 12 sqrt(3) " i

#### Explanation:

Rewrite as follow .... because we can't have a real answer if we have negative number under the radical

3sqrt(-48) = 3sqrt(48*-1

Rewrite, to that 2 numbers multiply equal 48 but one of them is a perfect square

$= 3 \sqrt{16 \cdot 3 \cdot - 1}$

Take the square root of 16, and square of -1 and place it in the front as and multiply it to 3

$= 3 \cdot 4 \cdot i \sqrt{3}$

$= 12 i \sqrt{3}$

**$\sqrt{- 1} = i$