What is the square root of 108 in simplest radical form?

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Pluma Share
Jun 30, 2016

Answer:

#6sqrt3#

Explanation:

By factoring, we get

#sqrt108# #= sqrt[36*3]#

#36= 6^2# so it is a perfect square.
We can take it out of the radical sign.

#sqrt108# = #6sqrt3#

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Write your answer here...
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Answer

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Answer:

Explanation

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Dec 20, 2016

Answer:

#sqrt(108)=color(blue)(6sqrt(3))#

Explanation:

Decomposing #108# into factors one step at a time:
#108#
#color(white)("XXX")=2xx54#
#color(white)("XXX")=2xx2xx27#
#color(white)("XXX")=2xx2xx3xx9#
#color(white)("XXX")=2xx2xx3xx3xx3#
#color(white)("XXX")=2^2xx3^2xx3#

#sqrt(108) =sqrt(2^2xx3^2xx3)#
#color(white)("XXX")=sqrt(2^2)xxsqrt(3^2)xxsqrt(3)#
#color(white)("XXX")=2xx3xxsqrt(3)#
#color(white)("XXX")=6sqrt(3)#

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