Question

What is the following quotient? ^3 square root 60 over ^3 square root of 20

Answer 1

3sqrt(60) sqrt(4*15) sqrt(15) sqrt(15)(sqrt(5) sqrt(75)
------------- = ----------------- = ----------- or --------------------- = ---------------
3sqrt(20) sqrt(4*5) sqrt(5) sqrt(5)*sqrt(5) 5

sqrt(25)*sqrt(3) sqrt(3)
This reduces to ---------------------- = -------------
5

What exactly do you mean by " ^3 ?" That's not standard math'l notation.


Here's a different and better approach:

3 sqrt(60)
-------------- = sqrt(60/20) = sqrt(3) (answer)
3 sqrt(20)

Answer 2

`√(3)` is the required quotient.

Explanation:

We have been given the expression:

`(3√(60))/(3√(20))`

Cancel the common term which is 3 we will be left with

`(√(60))/(√(20))`

`√(60)` can be written as after prime factorization is:

`2√(15)`

And
`√(20)` can be written as after prime factorization is:

`2√(5)`

Hence, the given expression would become after 2 gets cancel from numerator and denominator:

`(√(3)\cdot √(5))/(√(5))`

Quotient is the answer we get after dividing numerator by denominator and cancel common term which is
`√(5)`

`√(3)` is the required quotient.