To find the equivalent of the given quotient [tex]\(\frac{\sqrt{30}}{\sqrt{5}}\)[/tex], we can use the property that [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex].
Let's apply this property step-by-step:
1. Write the Original Expression:
[tex]\[
\frac{\sqrt{30}}{\sqrt{5}}
\][/tex]
2. Apply the Property [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex]:
[tex]\[
\frac{\sqrt{30}}{\sqrt{5}} = \sqrt{\frac{30}{5}}
\][/tex]
3. Simplify the Fraction Inside the Square Root:
[tex]\[
\frac{30}{5} = 6
\][/tex]
4. Express the Result as a Square Root:
[tex]\[
\sqrt{\frac{30}{5}} = \sqrt{6}
\][/tex]
Thus, the equivalent expression for [tex]\(\frac{\sqrt{30}}{\sqrt{5}}\)[/tex] is [tex]\(\sqrt{6}\)[/tex].
Comparing this with the given choices:
- A. 36 (Incorrect)
- B. [tex]\(-\sqrt{6}\)[/tex] (Incorrect)
- C. 6 (Incorrect)
- D. -6 (Incorrect)
- E. [tex]\(\sqrt{6}\)[/tex] (Correct)
Therefore, the correct choice is [tex]\( \boxed{\sqrt{6}} \)[/tex].
