Question

What is the square root of 14 divided by the square root of 45?

Answer 1

(Nothing really pretty)
`sqrt(14)/sqrt(45) = sqrt(21)/9`

Explanation:

`sqrt(14)/sqrt(45)`

Factoring:
`color(white)("XXXX")=(cancel(sqrt(2))*sqrt(7))/(sqrt(3)*sqrt(3)*sqrt(3)*cancel(sqrt(2)))`

Simplifying:
`color(white)("XXXX")=sqrt(7)/(3sqrt(3))`

Rationalizing the denominator (by multiplying both numerator and denominator by `(sqrt(3))`
`color(white)("XXXX")=sqrt(21)/9`