To simplify [tex]\(\sqrt{45}\)[/tex], we need to factorize 45 in such a way that one of the factors is a perfect square. Let's go through the steps:
1. Factorize 45:
[tex]\(45 = 9 \times 5\)[/tex]
2. Rewrite [tex]\(\sqrt{45}\)[/tex] using this factorization:
[tex]\[
\sqrt{45} = \sqrt{9 \times 5}
\][/tex]
3. Use the property of square roots, which states that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{45} = \sqrt{9} \times \sqrt{5}
\][/tex]
4. Since [tex]\(\sqrt{9} = 3\)[/tex], we can further simplify:
[tex]\[
\sqrt{45} = 3 \times \sqrt{5}
\][/tex]
So, the simplified form of [tex]\(\sqrt{45}\)[/tex] is [tex]\(3 \sqrt{5}\)[/tex].
Thus, the correct answer is:
D. [tex]\(3 \sqrt{5}\)[/tex]
