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

1 Answer
Mar 14, 2016

Answer:

#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!