a) √3 x √15
b) √32 x √24
c) 2√5 x 5√2
Remember that $\displaystyle \sqrt{ab}=\sqrt{a}\times\sqrt{b}$
And that $\displaystyle \sqrt{x}\times\sqrt{x}=x$
1) $\displaystyle \sqrt{15}=\sqrt{3}\times\sqrt{5}$
so $\displaystyle \sqrt{15}\times\sqrt{3}$
$\displaystyle =\sqrt{3}\times\sqrt{3}\times\sqrt{5}$
How would this simplify?
2)$\displaystyle \sqrt{32}$
$\displaystyle =\sqrt{16}\times\sqrt{2}$
$\displaystyle =4\times\sqrt{2}$
And
$\displaystyle \sqrt{24}$
$\displaystyle =\sqrt{4}\times\sqrt{6}$
$\displaystyle =2\times\sqrt{6}$
Substitute these into the equation and then simplification should become clear.
3)Write this as:
$\displaystyle 2\times5\times\sqrt{2}\times\sqrt{5} $
Simplifying from here should be straightforward.
Reply if you are still stuck and I'll try to be of more assistance.