To simplify [tex]\(\sqrt{80}\)[/tex], follow these steps:
1. Factorize 80 into its prime factors:
[tex]\[
80 = 2^4 \times 5
\][/tex]
2. Rewrite [tex]\(\sqrt{80}\)[/tex] using these prime factors:
[tex]\[
\sqrt{80} = \sqrt{2^4 \times 5}
\][/tex]
3. Use the property of square roots, which states that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{2^4 \times 5} = \sqrt{2^4} \times \sqrt{5}
\][/tex]
4. Find the square root of [tex]\(2^4\)[/tex]:
[tex]\[
\sqrt{2^4} = \sqrt{16} = 4
\][/tex]
5. Combine the results:
[tex]\[
\sqrt{80} = 4 \times \sqrt{5}
\][/tex]
Thus, the simplification of [tex]\(\sqrt{80}\)[/tex] is [tex]\(4 \sqrt{5}\)[/tex].
Looking at the given options:
- A. [tex]\(16 \sqrt{5}\)[/tex]
- B. [tex]\(5 \sqrt{4}\)[/tex]
- C. [tex]\(4 \sqrt{5}\)[/tex]
- D. [tex]\(20 \sqrt{4}\)[/tex]
The correct answer is:
C. [tex]\(4 \sqrt{5}\)[/tex]
