Question

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

Answer 1

`1/3`

Explanation:

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

Answer 2

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`