How do you simplify #sqrt(12/27)*sqrt(1/4)#?

2 Answers
May 14, 2017

Answer:

#1/3#

Explanation:

#sqrt(12/27)*sqrt(1/4) = (sqrt(4)*sqrt(3))/(sqrt(9)*sqrt(3)*sqrt(4))#
# = 1/sqrt(9)#
# = 1/3#

May 14, 2017

Answer:

See a solution process below:

Explanation:

First, we can combine the radicals using this rule:

#sqrt(a) * sqrt(b) = sqrt(a * b)#

#sqrt(12/27) * sqrt(1/4) => sqrt(12/27 * 1/4)#

We can rewrite the term in the radical and cancel common terms:

#sqrt(12/27 * 1/4) => sqrt((12 * 1)/(27 * 4)) => sqrt((4 * 3)/(9 * 3 * 4)) =>#

#sqrt((color(red)(cancel(color(black)(4))) * color(blue)(cancel(color(black)(3))))/(9 * color(blue)(cancel(color(black)(3))) * color(red)(cancel(color(black)(4))))) => sqrt(1/9) => 1/3#