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)#