Answered

Select the correct answer.

Simplify:
[tex]\sqrt{45}[/tex]

A. [tex]3 \sqrt{5}[/tex]

B. [tex]15 \sqrt{3}[/tex]

C. [tex]9 \sqrt{5}[/tex]

D. [tex]3 \sqrt{5}[/tex]



Answer :

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]