How do you simplify #sqrt3*sqrt27#?

2 Answers
Jun 13, 2016

Answer:

#= 9#

Explanation:

#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#

Jun 14, 2016

Answer:

= #sqrt81 = 9#

Explanation:

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

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

= #sqrt81#

#=9#