Question

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

Answer 1

Answer: D. $3\sqrt{2}$

Step-by-step explanation:

The given fraction : $\dfrac{6}{\sqrt{2}}$

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

So , we rationalize it by multiplying $\sqrt{2}$ to the numerator and the denominator , we get

$\dfrac{6}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}=\dfrac{6\sqrt{2}}{2}}\\\\=\dfrac{2\times3\times\sqrt{2}}{2}\\\\=3\sqrt{2}$  [Cancel 2 from the numerator and the denominator.]

Hence, the choice is equivalent to the given fraction = $3\sqrt{2}$

Hence, the correct option is D. $3\sqrt{2}$

Answer 2

Answer:

$\boxed{\text{D. }3\sqrt{2}}$

Step-by-step explanation:

Multiply numerator and denominator by √2

$\dfrac{6}{\sqrt{2}} = \dfrac{6}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\= \dfrac{6\sqrt{2}}{2}\\\\= \boxed{3\sqrt{2}}$