How do you simplify sqrt(12/27)*sqrt(1/4)√1227⋅√14?

2 Answers
Aymeric D.
May 14, 2017

1/313

Explanation:

sqrt(12/27)*sqrt(1/4) = (sqrt(4)*sqrt(3))/(sqrt(9)*sqrt(3)*sqrt(4))√1227⋅√14=√4⋅√3√9⋅√3⋅√4
= 1/sqrt(9)=1√9
= 1/3=13

smendyka
May 14, 2017

See a solution process below:

Explanation:

First, we can combine the radicals using this rule:

sqrt(a) * sqrt(b) = sqrt(a * b)√a⋅√b=√a⋅b

sqrt(12/27) * sqrt(1/4) => sqrt(12/27 * 1/4)√1227⋅√14⇒√1227⋅14

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)) =>√1227⋅14⇒√12⋅127⋅4⇒√4⋅39⋅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

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1701 views around the world
You can reuse this answer
Creative Commons License