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

2 Answers
Mar 24, 2015

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

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)#