How do you simplify #sqrt(54)#?

1 Answer
Alan P.
Jun 30, 2015

#sqrt(54) = 3sqrt(6)#

Explanation:

Factor #54# into primes:
#color(white)("XXXX")##54=2*27#
#color(white)("XXXX")##=2*3*9#
#color(white)("XXXX")##=2*3*3*3#

Grouping pairs of identical factors:
#color(white)("XXXX")##54 = 3^2*3*2#
#color(white)("XXXX")##=3^2*6#

#sqrt(54) = sqrt(3^2*6)#
#color(white)("XXXX")##=sqrt(3^2)*sqrt(6)#

#color(white)("XXXX")##=3sqrt(6)#

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