How do you simplify #sqrt27 * sqrt135 #?

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Answer 1 · 2016-04-19T05:28:57

#=27 sqrt ( 5 #

#sqrt27 * sqrt135#

Simplifying each of the terms:
#sqrt27 = sqrt ( 3*3*3) = sqrt(3^2 *3 ) = color(green)(3 sqrt3#

#sqrt135 = sqrt ( 3 * 3 * 3 * 5) = sqrt ( 3^2 * 15) = color(green)(3 sqrt15#

#sqrt27 * sqrt135 = color(green)(3 sqrt3) * color(green)(3 sqrt15#

#= 3 * 3 * sqrt 3 * sqrt15#

#=9* sqrt 3 * sqrt15#

#=9* sqrt (3 * 15#

#=9* sqrt (45#

#=9* sqrt (3 ^2 * 5 #

#=9* 3 sqrt ( 5 #

#=27 sqrt ( 5 #