Question

Which choices are equivalent to the quotient below? Check all that apply.A.B.5C.D.E.F.

Answer 1

Given:

The given quotient is,

$\frac{\sqrt{50}}{\sqrt{10}}$

Required:

To check all that are equivalent to the given quotient.

Answer:

We have the quotient given by,

$\frac{\sqrt{50}}{\sqrt{10}}$

Then squaring on numerator and denominator, we get,

$\begin{gathered} \frac{(\sqrt{50})^2}{(\sqrt{10})^2} \\ =\frac{50}{10} \\ =5 \end{gathered}$

Next,the given quotient can also be written as:

$\begin{gathered} \frac{\sqrt{50}}{\sqrt{10}} \\ =\sqrt{\frac{50}{10}} \\ =\sqrt{5} \end{gathered}$

Now, dividing by 2 on both numerator and denominator inside the square root, we get,

$\begin{gathered} \frac{\sqrt{\frac{50}{2}}}{\sqrt{\frac{10}{2}}} \\ =\frac{\sqrt{25}}{\sqrt{5}} \end{gathered}$

Final Answer:

The given quotient is equivalent to

$\begin{gathered} 5 \\ \sqrt{5} \\ \frac{\sqrt{25}}{\sqrt{5}} \end{gathered}$

Options B,D and F are correct.