How do you simplify #sqrt(54)#?

1 Answer
Jun 30, 2015

Answer:

#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)#