Question

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

Answer 1

Answer:

$\sqrt{3}$ is the required quotient.

Step-by-step explanation:

We have been given the expression:

$\frac{3\sqrt{60}}{3\sqrt{20}}$

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

$\frac{\sqrt{60}}{\sqrt{20}}$

$\sqrt{60}$ can be written as after prime factorization is:

$2\sqrt{15}$

And $\sqrt{20}$ can be written as after prime factorization is:

$2\sqrt{5}$

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

$\frac{\sqrt{3}\cdot \sqrt{5}}{\sqrt{5}}$

Quotient is the answer we get after dividing numerator by denominator and cancel common term which is $\sqrt{5}$

$\sqrt{3}$ is the required quotient.

Answer 2

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)