How do you simplify #sqrt3*sqrt27#?

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Answer 1 · 2016-06-13T03:09:10

#= 9#

#sqrt3 * sqrt27#

#sqrt27# can be simplified by prime factorisation. (expressing a number as a product of its prime factors)

#sqrt27= sqrt ( 3 * 3 * 3 ) = sqrt (3 * 3^2) = color(blue)(3sqrt3 #

The expression can now be written as:
#sqrt3 * sqrt27 = sqrt 3 * color(blue)(3sqrt3#

#= 3 * sqrt 3 * color(blue)(sqrt3#

#= 3 * 3 #

#= 9#

Answer 2 · 2016-06-14T20:28:17

= #sqrt81 = 9#

When multiplying or dividing with roots, two roots can be combined into one root.

#sqrt3 xx sqrt 27 = sqrt(3 xx27)#

= #sqrt81#

#=9#