To simplify the expression [tex]\(\sqrt{45}\)[/tex]:
1. First, we identify the factors of 45:
[tex]\[
45 = 9 \times 5
\][/tex]
2. Next, we use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{45} = \sqrt{9 \times 5}
\][/tex]
3. We know that 9 is a perfect square, and [tex]\(\sqrt{9} = 3\)[/tex]:
[tex]\[
\sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5}
\][/tex]
4. Substituting the value of [tex]\(\sqrt{9}\)[/tex]:
[tex]\[
\sqrt{9} \times \sqrt{5} = 3 \times \sqrt{5}
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\sqrt{45} = 3 \times \sqrt{5}
\][/tex]
