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,

`(√(50))/(√(10))`

Required:

To check all that are equivalent to the given quotient.

Answer:

We have the quotient given by,

`(√(50))/(√(10))`

Then squaring on numerator and denominator, we get,

`\begin{gathered} ((√(50))^2)/((√(10))^2) \\ =(50)/(10) \\ =5 \end{gathered}`

Next,the given quotient can also be written as:

`\begin{gathered} (√(50))/(√(10)) \\ =\sqrt{(50)/(10)} \\ =√(5) \end{gathered}`

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

`\begin{gathered} \frac{\sqrt{(50)/(2)}}{\sqrt{(10)/(2)}} \\ =(√(25))/(√(5)) \end{gathered}`

Final Answer:

The given quotient is equivalent to

`\begin{gathered} 5 \\ √(5) \\ (√(25))/(√(5)) \end{gathered}`

Options B,D and F are correct.