Question

How do you simplify `sqrt(120x^4)/sqrt(6x)`?

Answer 1

`2xsqrt(5x)-= 2sqrt(5x^3)`

I would suggest that `2xsqrt(5x)` may be the better choice of the two!

Explanation:

Given:`" "sqrt(122x^4)/sqrt(6x)`

Prime factors of 6 are: 2 and 3

#Prime factors of 120 are:2^2, 2, 3,5

So the given expression can be written as:

`sqrt(2^2xx2xx3xx5xx(x^2)^2)/(sqrt(2xx3xxx)`

This gives:

`2x^2xx(sqrt(2)xxsqrt(3)xxsqrt(5))/(sqrt(2)xxsqrt(3)xxsqrt(x))`

`2x^2xxsqrt(2)/sqrt(2) xxsqrt(3)/sqrt(3)xxsqrt(5)/sqrt(x)`

`2x^2xxsqrt(5)/sqrt(x)`

Multiply by 1 but in the form of `1=sqrt(x)/sqrt(x)`

`2x^2xxsqrt(5)/sqrt(x)xxsqrt(x)/sqrt(x)`

`2x^2xxsqrt(5x)/x`

`2xsqrt(5x)-= 2sqrt(5x^3)`

I would suggest that `2xsqrt(5x)` may be the better choice of the two!