How do you simplify #sqrt75*sqrt60#?

1 Answer
Johnson Z.
Feb 1, 2016

#30sqrt(5)#

Explanation:

Recall that a #color(blue)("perfect square")# is the product of squaring a whole number.

For example:

#2^2=color(blue)4#

#3^2=color(blue)9#

#5^2=color(blue)25#

#6^2=color(blue)36#

When you simplify a radical, you must first break it down using #color(blue)("perfect square")# numbers. For example, in your case:

#sqrt(75)*sqrt(60)#

#=sqrt(color(blue)25*3)*sqrt(color(blue)4*15)#

The square root of #color(blue)25# is #color(red)5#, so you can bring the 25 out of the square root sign and write a #5# instead. Similarly, the square root of #color(blue)4# is #color(red)2#, so you can also bring the #4# out of the square root sign and write a #2# instead.

#=color(red)5color(green)(sqrt(3))*color(red)2color(green)(sqrt(15))#

Multiply.

#=(color(red)5*color(red)2)(color(green)(sqrt(3))*color(green)(sqrt(15)))#

#=10sqrt(45)#

Since #sqrt(45)# can be simplified even further:

#=10sqrt(color(blue)9*5)#

Simplify.

#=10*color(red)3sqrt(5)#

#=30sqrt(5)#

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