How do you simplify #sqrt675-sqrt27#?

2 Answers
Mar 12, 2018

Answer:

#12sqrt3#

Explanation:

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

Mar 12, 2018

Answer:

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

Explanation:

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#