From everyday questions to specialized queries, IDNLearn.com has the answers. Our platform offers comprehensive and accurate responses to help you make informed decisions on any topic.
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]
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.