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Which choice is equivalent to the quotient below?

[tex]\[
\frac{\sqrt{32}}{\sqrt{2}}
\][/tex]

A. 4
B. 2
C. [tex]$\sqrt{16}$[/tex]
D. [tex]$\frac{\sqrt{2}}{2}$[/tex]


Sagot :

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