To simplify [tex]\(\sqrt{99}\)[/tex], we can follow these steps:
1. Factorize 99 into its prime factors:
[tex]\[
99 = 3 \times 3 \times 11
\][/tex]
which can be written as:
[tex]\[
99 = 3^2 \times 11
\][/tex]
2. Express the square root of 99 in terms of these factors:
[tex]\[
\sqrt{99} = \sqrt{3^2 \times 11}
\][/tex]
3. Utilize the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{99} = \sqrt{3^2 \times 11} = \sqrt{3^2} \times \sqrt{11}
\][/tex]
4. Simplify [tex]\(\sqrt{3^2}\)[/tex]:
[tex]\[
\sqrt{3^2} = 3
\][/tex]
5. Combine the simplified parts:
[tex]\[
\sqrt{99} = 3 \times \sqrt{11}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{99}\)[/tex] is:
[tex]\[
\boxed{3\sqrt{11}}
\][/tex]
