Question

multiply and simplify by factoring
sqrt{?}45 * sqrt{?}375

Answer 1

\[\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}\]\[similarly, \sqrt{375} = \sqrt{3*125} =\sqrt{15*25}=\sqrt{15}*\sqrt{25}=5\sqrt{15}\]\[3\sqrt{5}*5\sqrt{15}=15\sqrt{5*15}=15\sqrt{75}=15\sqrt{3*25}=75\sqrt{3}\]Apologies for running through every step; just ensuring that the method can be followed without confusion and hopefully, as such, you'd be fine come exam time.

Answer 2

Naturally, you could multiply \[\sqrt{45} and \sqrt{375} geting \sqrt{45*375}\]and split into sqrt{75^2 * 3}
It's just neater to simplify, multiply and then simplify again in most situations.