How do you simplify sqrt15 * sqrt45?

1 Answer
May 1, 2016

15sqrt(3)

Explanation:

Given,

sqrt(15)*sqrt(45)

Break down each radical using square numbers. Since sqrt(15) cannot be simplified any further, it is left as is.

=sqrt(15)*sqrt(9*5)

Since sqrt(9)=3, you can simplify the second radical.

=sqrt(15)*3sqrt(5)

Now that the second radical is simplified, multiply it by the first radical.

=3sqrt(15*5)

=3sqrt(75)

Break down sqrt(75) using square numbers.

=3sqrt(25*3)

Since sqrt(25)=5, you can simplify the radical.

=3*5sqrt(3)

=color(green)(|bar(ul(color(white)(a/a)color(black)(15sqrt(3))color(white)(a/a)|)))