Question

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

Answer 1

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

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

`(2√(2))/(x^3)`

Explanation:

`\sqrt{(8)/(x^6) }`

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

`(√(8) )/(√(x^6) )`

`√(8) =√(4*2) =2√(2)`

`√(x^6) =√(x^3*x^3) =x^3`

Replace it in our problem

`(2√(2))/(x^3)`