How do you simplify sqrt27 * sqrt135 √27⋅√135?

1 Answer
Don't Memorise
Apr 19, 2016

=27 sqrt ( 5 =27√5

Explanation:

sqrt27 * sqrt135√27⋅√135

Simplifying each of the terms:
sqrt27 = sqrt ( 3*3*3) = sqrt(3^2 *3 ) = color(green)(3 sqrt3√27=√3⋅3⋅3=√32⋅3=3√3

sqrt135 = sqrt ( 3 * 3 * 3 * 5) = sqrt ( 3^2 * 15) = color(green)(3 sqrt15√135=√3⋅3⋅3⋅5=√32⋅15=3√15

sqrt27 * sqrt135 = color(green)(3 sqrt3) * color(green)(3 sqrt15√27⋅√135=3√3⋅3√15

= 3 * 3 * sqrt 3 * sqrt15=3⋅3⋅√3⋅√15

=9* sqrt 3 * sqrt15=9⋅√3⋅√15

=9* sqrt (3 * 15=9⋅√3⋅15

=9* sqrt (45=9⋅√45

=9* sqrt (3 ^2 * 5 =9⋅√32⋅5

=9* 3 sqrt ( 5 =9⋅3√5

=27 sqrt ( 5 =27√5

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