How do you simplify #sqrt84 * sqrt28#?

1 Answer
Apr 30, 2016

#sqrt(84)*sqrt(28)=sqrt(28^2*3)=28sqrt(3)#

Explanation:

Here's a factor tree for #28#:

#color(white)(0000)28#
#color(white)(000)"/"color(white)(00)"\"#
#color(white)(00)2color(white)(000)14#
#color(white)(00000)"/"color(white)(00)"\"#
#color(white)(0000)2color(white)(0000)7#

So: #28 = 2^2*7#

#color(white)()#
Here's a factor tree for #84#:

#color(white)(0000)84#
#color(white)(000)"/"color(white)(00)"\"#
#color(white)(00)2color(white)(000)42#
#color(white)(00000)"/"color(white)(00)"\"#
#color(white)(0000)2color(white)(000)21#
#color(white)(0000000)"/"color(white)(00)"\"#
#color(white)(000000)3color(white)(0000)7#

So: #84 = 2^2*3*7 = 28*3#

#color(white)()#
So:

#sqrt(84)*sqrt(28)=sqrt(84*28)=sqrt(28^2*3)=28sqrt(3)#