How do you simplify $5 sqrt5 * 3sqrt3$ ?

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Answer 1 · 2015-06-23T23:46:19

I found:
$15sqrt(15)$

Multiply the number outside AND inside the roots as:

$5sqrt(5)*3sqrt(3)=5*3sqrt(5*3)=15sqrt(15)$

Answer 2 · 2015-06-23T23:47:15

$5sqrt(5)*3sqrt(3) = 15 sqrt(15)$

$5sqrt(5)$ means $5*sqrt(5)$
and
$3sqrt(3)$ means $3*sqrt(3)$

So $5sqrt(5)*3sqrt(3)$
can be written as $5*sqrt(5)*3*sqrt(3)$

This can be re-arranged as
$color(white)("XXXX")$ $(5*3)* (sqrt(5)*sqrt(3))$

and since $sqrt(a)*sqrt(b) = sqrt(a*b)$

$color(white)("XXXX")$ $5sqrt(5)*3sqrt(3) = 15 sqrt(15)$

How do you simplify 5 sqrt5 * 3sqrt35 sqrt5 * 3sqrt3?