How do you simplify 5sqrt5 * 3sqrt3?

Mar 24, 2015

You can write:
$5 \cdot 3 \cdot \sqrt{5 \cdot 3} = 15 \sqrt{15}$

Mar 24, 2015

$5 a \cdot 3 b$?

What this really means is
$5 \times a \times 3 \times b$
which can be rewritten as
$5 \times 3 \times a \times b$
$= 15 \left(a \times b\right)$

$a = \sqrt{5}$ and $b = \sqrt{3}$
in general $\sqrt{p} \times \sqrt{q} = \sqrt{p q}$
$\sqrt{5} \times \sqrt{3} = \sqrt{15}$
$5 \sqrt{5} \cdot 3 \sqrt{3} = 15 \sqrt{15}$