How do you multiply (15sqrt( 8x^16)) /( 5 sqrt( 2x^4))?

May 2, 2015

We start by taking all squares from under the root.

Since $8 = 2 \cdot 2 \cdot 2 = 2 \cdot {2}^{2}$ and ${x}^{16} = {\left({x}^{8}\right)}^{2}$
And ${x}^{4} = {\left({x}^{2}\right)}^{2}$

We can take out these squares (unsquared of course), and in both cases only a single $2$ will be left under the root:

$= \frac{15 \cdot 2 \cdot {x}^{4} \sqrt{2}}{5 \cdot {x}^{2} \sqrt{2}} = \frac{30 \cdot {x}^{2} \cdot {x}^{2} \cdot \sqrt{2}}{5 \cdot {x}^{2} \cdot \sqrt{2}}$

Now we can cancel out the ${x}^{2}$ and the $\sqrt{2}$:

$= \frac{30 \cdot {x}^{2}}{5} = 6 {x}^{2}$