How do you simplify #sqrt675-sqrt27#?

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Answer 1 · 2018-03-12T04:57:24

#12sqrt3#

#sqrt675=sqrt{225\times3}=15sqrt3#
#sqrt27=sqrt{9\times3}=3sqrt3#
#sqrt675-sqrt27=15sqrt3-3sqrt3=12sqrt3#

Answer 2 · 2018-03-12T06:14:46

#sqrt(675)-sqrt(27)=color(blue)(12sqrt3#

Simplify:

#sqrt(675)-sqrt(27)#

Prime factorize each radicand.

#sqrt(3*3^2*5^2)-sqrt(3^2*3)#

Apply the rule: #sqrt(a^2)=a#

#3*5sqrt3-3sqrt3#

Simplify.

#15sqrt3-3sqrt3#

Numbers that have the same square root can be added or subtracted.

#15sqrt3-3sqrt3=#

#12sqrt3#