Let's say I am to multiply $3x^2$ by ${\sqrt 8}$.
Which answer is true and why?
$3 {\sqrt 8x^2}$
or
$\endgroup$ 5$3x^2 {\sqrt 8}$
1 Answer
$\begingroup$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, $$3\sqrt8x^2=abc=(ab)c=a(bc)=a(cb)=acb=3x^2\sqrt8$$
$\endgroup$ 2
