To find the expression that is equivalent to [tex]\(\sqrt{45}\)[/tex], let's simplify [tex]\(\sqrt{45}\)[/tex].
First, we factorize 45 into its prime factors:
[tex]\[
45 = 9 \times 5
\][/tex]
Thus,
[tex]\[
\sqrt{45} = \sqrt{9 \times 5}
\][/tex]
Since the square root of a product is the product of the square roots:
[tex]\[
\sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5}
\][/tex]
We know the square root of 9 is 3:
[tex]\[
\sqrt{9} = 3
\][/tex]
Therefore:
[tex]\[
\sqrt{45} = 3 \times \sqrt{5} = 3\sqrt{5}
\][/tex]
Now, let's look at the given answer choices:
A. [tex]\(3 \sqrt{5}\)[/tex]
B. [tex]\(9 \sqrt{5}\)[/tex]
C. [tex]\(5 \sqrt{3}\)[/tex]
D. [tex]\(5 \sqrt{9}\)[/tex]
Comparing our simplified expression [tex]\(\sqrt{45} = 3\sqrt{5}\)[/tex] with the choices provided, we see that the correct choice is:
A. [tex]\(3 \sqrt{5}\)[/tex]
The expression [tex]\(\sqrt{45}\)[/tex] is equivalent to [tex]\(3 \sqrt{5}\)[/tex].
