Multiplying radicals by variables

Question

Let's say I am to multiply $3x^2$ by ${\sqrt 8}$.
Which answer is true and why?

$3 {\sqrt 8x^2}$

or

$3x^2 {\sqrt 8}$

Answer 1

Are the same.

You can use the following laws.

For all reals $a$, $b$ and $c$ we have $$ab=ba$$ and $$(ab)c=a(bc).$$ Now, let $3=a$, $\sqrt8=b$ and $x^2=c$.

Thus, $$3\sqrt8x^2=abc=(ab)c=a(bc)=a(cb)=acb=3x^2\sqrt8$$