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

Mar 14, 2016

$2 x \sqrt{5 x} \equiv 2 \sqrt{5 {x}^{3}}$

I would suggest that $2 x \sqrt{5 x}$ may be the better choice of the two!

#### Explanation:

Given:$\text{ } \frac{\sqrt{122 {x}^{4}}}{\sqrt{6 x}}$

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:

$2 {x}^{2} \times \frac{\sqrt{2} \times \sqrt{3} \times \sqrt{5}}{\sqrt{2} \times \sqrt{3} \times \sqrt{x}}$

$2 {x}^{2} \times \frac{\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{3}}{\sqrt{3}} \times \frac{\sqrt{5}}{\sqrt{x}}$

$2 {x}^{2} \times \frac{\sqrt{5}}{\sqrt{x}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{x}}{\sqrt{x}}$

$2 {x}^{2} \times \frac{\sqrt{5}}{\sqrt{x}} \times \frac{\sqrt{x}}{\sqrt{x}}$

$2 {x}^{2} \times \frac{\sqrt{5 x}}{x}$

$2 x \sqrt{5 x} \equiv 2 \sqrt{5 {x}^{3}}$

I would suggest that $2 x \sqrt{5 x}$ may be the better choice of the two!