How do you simplify #sqrt15 * sqrt45#?

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Answer 1 · 2016-05-01T15:25:07

#15sqrt(3)#

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)|)))#