To determine which expression is equivalent to [tex]\(\sqrt{45}\)[/tex], let's go through the simplification step by step.
1. Prime factorization of 45:
[tex]\[
45 = 3 \times 3 \times 5 = 3^2 \times 5
\][/tex]
2. Simplifying the square root:
[tex]\[
\sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5} = 3 \times \sqrt{5} = 3\sqrt{5}
\][/tex]
Therefore, the correct expression that is equivalent to [tex]\(\sqrt{45}\)[/tex] is:
A. [tex]\(3 \sqrt{5}\)[/tex]
