To determine which choice is equivalent to the quotient [tex]\(\frac{\sqrt{36}}{\sqrt{4}}\)[/tex], we'll follow these steps:
1. Evaluate the square roots:
- [tex]\(\sqrt{36}\)[/tex] is the number which, when multiplied by itself, gives 36. Since [tex]\(6 \times 6 = 36\)[/tex], we have [tex]\(\sqrt{36} = 6\)[/tex].
- [tex]\(\sqrt{4}\)[/tex] is the number which, when multiplied by itself, gives 4. Since [tex]\(2 \times 2 = 4\)[/tex], we have [tex]\(\sqrt{4} = 2\)[/tex].
2. Form the quotient:
- Now we substitute the evaluated square roots into the quotient:
[tex]\[
\frac{\sqrt{36}}{\sqrt{4}} = \frac{6}{2}
\][/tex]
3. Simplify the quotient:
- Dividing 6 by 2, we get:
[tex]\[
\frac{6}{2} = 3
\][/tex]
Thus, the value of the quotient [tex]\(\frac{\sqrt{36}}{\sqrt{4}}\)[/tex] is 3.
Given the choices:
- A. 9
- B. [tex]\(\sqrt{12}\)[/tex]
- C. 3
- D. [tex]\(\frac{\sqrt{2}}{2}\)[/tex]
The correct answer is C. [tex]\(3\)[/tex].
