Question

Which choice is equivalent to the fraction below? Hint: Rationalize the denominator and simplify.

Please show work.

Answer 1

Answer: D.
`3√(2)`

Explanation:

The given fraction :
`(6)/(√(2))`

Here, the denominator is in radical form which makes it not an simplified form.

So , we rationalize it by multiplying
`√(2)` to the numerator and the denominator , we get

`(6)/(√(2))*(√(2))/(√(2)=(6√(2))/(2))\\\\=(2*3*√(2))/(2)\\\\=3√(2)` [Cancel 2 from the numerator and the denominator.]

Hence, the choice is equivalent to the given fraction =
`3√(2)`

Hence, the correct option is D.
`3√(2)`

Answer 2

`\boxed{\text{D. }3√(2)}`

Explanation:

Multiply numerator and denominator by √2

`(6)/(√(2)) = (6)/(√(2)) * (√(2))/(√(2))\\\\= (6√(2))/(2)\\\\= \boxed{3√(2)}`