How do you simplify 5sqrt5 * 3sqrt3?

2 Answers
Gió
Mar 24, 2015

You can write:
5*3*sqrt(5*3)=15sqrt(15)

Alan P.
Mar 24, 2015

Suppose we start with a simpler problem. What is
5a * 3b?

What this really means is
5 xx a xx 3 xx b
which can be rewritten as
5 xx 3 xx a xx b
= 15 (a xx b)

Since in your original question
a = sqrt(5) and b = sqrt(3)
we only need to know that
in general sqrt(p) xx sqrt(q) = sqrt(pq)
or in particular that
sqrt(5) xx sqrt(3) = sqrt(15)

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

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