How do you simplify $5 \sqrt{5} \cdot 3 \sqrt{3}$ $5 sqrt5 * 3sqrt3$ ?

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Answer 1 · 2015-06-23T23:46:19

I found:
$15 \sqrt{15}$ $15sqrt(15)$

Multiply the number outside AND inside the roots as:

$5 \sqrt{5} \cdot 3 \sqrt{3} = 5 \cdot 3 \sqrt{5 \cdot 3} = 15 \sqrt{15}$ $5sqrt(5)*3sqrt(3)=5*3sqrt(5*3)=15sqrt(15)$

Answer 2 · 2015-06-23T23:47:15

$5 \sqrt{5} \cdot 3 \sqrt{3} = 15 \sqrt{15}$ $5sqrt(5)*3sqrt(3) = 15 sqrt(15)$

$5 \sqrt{5}$ $5sqrt(5)$ means $5 \cdot \sqrt{5}$ $5*sqrt(5)$
and
$3 \sqrt{3}$ $3sqrt(3)$ means $3 \cdot \sqrt{3}$ $3*sqrt(3)$

So $5 \sqrt{5} \cdot 3 \sqrt{3}$ $5sqrt(5)*3sqrt(3)$
can be written as $5 \cdot \sqrt{5} \cdot 3 \cdot \sqrt{3}$ $5*sqrt(5)*3*sqrt(3)$

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

and since $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ $sqrt(a)*sqrt(b) = sqrt(a*b)$

$XXXX$ $color(white)("XXXX")$ $5 \sqrt{5} \cdot 3 \sqrt{3} = 15 \sqrt{15}$ $5sqrt(5)*3sqrt(3) = 15 sqrt(15)$

How do you simplify 5√5⋅3√35 sqrt5 * 3sqrt3?