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Answer :
Let's simplify the expression [tex]\(\sqrt{8} \times 320 \times x^2 \times y^5\)[/tex] step by step.
1. Simplify [tex]\(\sqrt{8}\)[/tex]:
- [tex]\(\sqrt{8}\)[/tex] can be rewritten as [tex]\(\sqrt{4 \times 2}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we have [tex]\(\sqrt{8} = 2 \sqrt{2}\)[/tex].
2. Rewrite the Expression:
- Substitute [tex]\(\sqrt{8}\)[/tex] with [tex]\(2 \sqrt{2}\)[/tex] in the original expression:
[tex]\[
2 \sqrt{2} \times 320 \times x^2 \times y^5
\][/tex]
3. Combine Constants:
- Multiply [tex]\(2\)[/tex] by [tex]\(320\)[/tex]:
[tex]\[
2 \times 320 = 640
\][/tex]
- So the expression becomes:
[tex]\[
640 \sqrt{2} \times x^2 \times y^5
\][/tex]
4. Factorize Further (if possible):
- There is no more simplification possible beyond factoring the expression as per the given options.
Now, let's analyze the provided answer choices:
- Option a: [tex]\(8 x^9 y^2 \sqrt{5} 5 y^2\)[/tex]
- Option b: [tex]\(8 x^4 y y^6 5 y^2\)[/tex]
- Option c: [tex]\(4 x^9 y^2 \sqrt{7} 5 y^2\)[/tex]
- Option d: [tex]\(4 y y^{10 x y^2}\)[/tex]
Based on simplifications and the initial results, none of the options correctly represent the simplified expression of [tex]\(640 \sqrt{2} \times x^2 \times y^5\)[/tex]. So, the simplified form doesn't exactly match any of the given choices.
1. Simplify [tex]\(\sqrt{8}\)[/tex]:
- [tex]\(\sqrt{8}\)[/tex] can be rewritten as [tex]\(\sqrt{4 \times 2}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we have [tex]\(\sqrt{8} = 2 \sqrt{2}\)[/tex].
2. Rewrite the Expression:
- Substitute [tex]\(\sqrt{8}\)[/tex] with [tex]\(2 \sqrt{2}\)[/tex] in the original expression:
[tex]\[
2 \sqrt{2} \times 320 \times x^2 \times y^5
\][/tex]
3. Combine Constants:
- Multiply [tex]\(2\)[/tex] by [tex]\(320\)[/tex]:
[tex]\[
2 \times 320 = 640
\][/tex]
- So the expression becomes:
[tex]\[
640 \sqrt{2} \times x^2 \times y^5
\][/tex]
4. Factorize Further (if possible):
- There is no more simplification possible beyond factoring the expression as per the given options.
Now, let's analyze the provided answer choices:
- Option a: [tex]\(8 x^9 y^2 \sqrt{5} 5 y^2\)[/tex]
- Option b: [tex]\(8 x^4 y y^6 5 y^2\)[/tex]
- Option c: [tex]\(4 x^9 y^2 \sqrt{7} 5 y^2\)[/tex]
- Option d: [tex]\(4 y y^{10 x y^2}\)[/tex]
Based on simplifications and the initial results, none of the options correctly represent the simplified expression of [tex]\(640 \sqrt{2} \times x^2 \times y^5\)[/tex]. So, the simplified form doesn't exactly match any of the given choices.
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