To determine which choice is equivalent to [tex]\( \frac{\sqrt{32}}{\sqrt{2}} \)[/tex], let's simplify the expression step by step.
1. Start with the original expression:
[tex]\[
\frac{\sqrt{32}}{\sqrt{2}}
\][/tex]
2. Utilize properties of square roots to combine the expression under a single square root. Recall that [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex]:
[tex]\[
\frac{\sqrt{32}}{\sqrt{2}} = \sqrt{\frac{32}{2}}
\][/tex]
3. Perform the division inside the square root:
[tex]\[
\frac{32}{2} = 16
\][/tex]
Thus, the expression simplifies to:
[tex]\[
\sqrt{16}
\][/tex]
4. Find the square root of 16:
[tex]\[
\sqrt{16} = 4
\][/tex]
Therefore, the expression [tex]\( \frac{\sqrt{32}}{\sqrt{2}} \)[/tex] simplifies to 4.
Thus, the correct choice equivalent to the quotient [tex]\( \frac{\sqrt{32}}{\sqrt{2}} \)[/tex] is:
[tex]\[
\boxed{4}
\][/tex]
The corresponding choice is:
A. 4
