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Select the correct answer.

Simplify:
[tex]\[ \sqrt{80} \][/tex]

A. [tex]\(16 \sqrt{5}\)[/tex]
B. [tex]\(5 \sqrt{4}\)[/tex]
C. [tex]\(4 \sqrt{5}\)[/tex]
D. [tex]\(20 \sqrt{4}\)[/tex]


Sagot :

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]