To solve the problem of finding the equivalent value to the quotient [tex]\(\frac{\sqrt{45}}{\sqrt{9}}\)[/tex], let us proceed step by step.
1. Simplify the individual square roots:
- First, consider [tex]\(\sqrt{45}\)[/tex].
- To find [tex]\(\sqrt{45}\)[/tex], note that [tex]\(45\)[/tex] can be expressed as [tex]\(45 = 9 \times 5\)[/tex]. Therefore, [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}\)[/tex].
- Next, consider [tex]\(\sqrt{9}\)[/tex].
- Since [tex]\(9\)[/tex] is a perfect square, [tex]\(\sqrt{9} = 3\)[/tex].
2. Write the quotient with the simplified values:
- Now we substitute the simplified values back into the quotient:
[tex]\[
\frac{\sqrt{45}}{\sqrt{9}} = \frac{3\sqrt{5}}{3}
\][/tex]
3. Simplify the fraction:
- We can cancel the [tex]\(3\)[/tex] in the numerator and the denominator:
[tex]\[
\frac{3\sqrt{5}}{3} = \sqrt{5}
\][/tex]
Therefore, [tex]\(\frac{\sqrt{45}}{\sqrt{9}} = \sqrt{5}\)[/tex].
The correct choice is:
A. [tex]\(\sqrt{5}\)[/tex]
