To simplify the expression [tex]\(\sqrt{80}\)[/tex], let's follow these steps:
1. Factor 80 into its prime factors:
[tex]\( 80 = 16 \times 5 \)[/tex]
2. Rewrite the square root of the product:
[tex]\[
\sqrt{80} = \sqrt{16 \times 5}
\][/tex]
3. Use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{80} = \sqrt{16} \times \sqrt{5}
\][/tex]
4. Find the square root of 16:
[tex]\[
\sqrt{16} = 4
\][/tex]
5. Combine the results:
[tex]\[
\sqrt{80} = 4 \times \sqrt{5}
\][/tex]
6. Simplified form:
[tex]\[
\sqrt{80} = 4 \sqrt{5}
\][/tex]
Therefore, the correct answer is:
C. [tex]\(4 \sqrt{5}\)[/tex]
