How do you simplify -4sqrt12 times 3 sqrt8 ?

Jun 19, 2016

$- 48 \sqrt{6}$

Explanation:

you can write the equivalent expression:

$- 4 \sqrt{{2}^{2} \cdot 3} \cdot 3 \sqrt{{2}^{2} \cdot 2}$

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

$- 48 \sqrt{6}$

Jun 19, 2016

To solve this family of problems you have to see if the numbers in the root can be factorized.

$\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3}$

in the same way $\sqrt{8} = 2 \sqrt{2}$ (try it).

then we have:

$- 4 \sqrt{12} \setminus \times 3 \sqrt{8}$

$= - 4 \cdot 2 \cdot \sqrt{3} \setminus \times 3 \cdot 2 \cdot \sqrt{2}$

$= - 8 \sqrt{3} \setminus \times 6 \sqrt{2}$

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

$= - 48 \sqrt{6}$.