Question

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

Answer 1

We start by taking all squares from under the root.

Since `8=2*2*2=2*2^2` and `x^16=(x^8)^2`
And `x^4=(x^2)^2`

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

`=(15*2*x^4sqrt2)/(5*x^2sqrt2)=(30*x^2*x^2*sqrt2)/(5*x^2*sqrt2)`

Now we can cancel out the `x^2` and the `sqrt2`:

`=(30*x^2)/5=6x^2`