# Simplify? sqrt8 xx sqrt(48^3)

$\sqrt{8} \times \sqrt{{48}^{3}} = 384 \sqrt{6}$

#### Explanation:

$\sqrt{8} \times \sqrt{{48}^{3}}$

Because both terms are under a square root sign, we can combine them:

$\sqrt{8 \times {48}^{3}}$

Rather than doing the cube of 48 first, let's see that $8 = {2}^{3}$, and so we can combine again:

$\sqrt{{2}^{3} \times {48}^{3}} = \sqrt{{96}^{3}} = {96}^{\frac{3}{2}}$

I'll go ahead and cube now, then work on the square root after:

$\sqrt{884736} = \sqrt{16384 \times 54}$

(I kept dividing by 4 to find the 16384).

Note that ${2}^{14} = 16384$, and so $\sqrt{{2}^{14}} = {2}^{7} = 128$. Also, $54 = 9 \times 6$ and so $\sqrt{54} = 3 \sqrt{6}$

Putting it together, we get:

$\sqrt{884736} = \sqrt{16384 \times 54} = 128 \times 3 \times \sqrt{6} = 384 \sqrt{6}$