Question

Which expression is equivalent to square root 8/x^6? assume x > 0

Answer 1

Answer:

The equivalent expression is  (2 / x ^ 3) * sqrt (2)

Step-by-step explanation:

We have sqrt 8 / x ^ 6

 Rewriting the expression:

 =sqrt (8 / x ^ 6)

 =sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))

 =(2 / (x * x * x)) sqrt (2)

= (2 / x ^ 3) * sqrt (2)

We get finally

 (2 / x ^ 3) * sqrt (2)

Answer 2

Answer:

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

Step-by-step explanation:

$\sqrt{\frac{8}{x^6} }$

To simplify the given expression we take square root for the top and bottom

$\frac{\sqrt{8} }{\sqrt{x^6} }$

$\sqrt{8} =\sqrt{4*2} =2\sqrt{2}$

$\sqrt{x^6} =\sqrt{x^3*x^3} =x^3$

Replace it in our problem

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