Question
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Which expression is equivalent to 60x3−−−−√
?
(1 point)
Responses
4x215x−−−√
4 x squared square root of 15 x
2x230x−−−√
2 x squared square root of 30 x
2x15x−−−√
2 x square root of 15 x
30x3
30 x cubed
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Which expression is equivalent to 60x3−−−−√
?
(1 point)
Responses
4x215x−−−√
4 x squared square root of 15 x
2x230x−−−√
2 x squared square root of 30 x
2x15x−−−√
2 x square root of 15 x
30x3
30 x cubed
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Answers
GPT-4o mini
To simplify the expression \( 60\sqrt[3]{x} \), we'll first factor the number 60 and separate the radicals properly.
1. Factor 60:
\[
60 = 4 \times 15
\]
2. Write the expression:
\[
60\sqrt[3]{x} = 4\sqrt[3]{15} \cdot \sqrt[3]{x^3}
\]
3. Recognize that \(\sqrt[3]{x^3} = x\):
\[
= 4x\sqrt[3]{15}
\]
Let's check the responses given:
1. **4x²√15x**: This is incorrect due to the x² term.
2. **2x²√30x**: This is incorrect due to the x² term and the wrong number under the square root.
3. **2x√15x**: This could also be incorrect due to the form of x.
4. **30x³**: This is incorrect, as it's just a cubic term.
None of the provided responses seem to accurately transform the original expression \( 60\sqrt[3]{x} \). However, it appears that there may be a misunderstanding of how we should approach the simplification or interpretation of what's being asked.
Based on common sense and the multiple approaches above, please double-check the responses or reanalyze the question.
Until you find a response that matches what was simplified, it's possible none might be accurate, so verifying them against the derived expectations above could be key in understanding the simplification steps.
1. Factor 60:
\[
60 = 4 \times 15
\]
2. Write the expression:
\[
60\sqrt[3]{x} = 4\sqrt[3]{15} \cdot \sqrt[3]{x^3}
\]
3. Recognize that \(\sqrt[3]{x^3} = x\):
\[
= 4x\sqrt[3]{15}
\]
Let's check the responses given:
1. **4x²√15x**: This is incorrect due to the x² term.
2. **2x²√30x**: This is incorrect due to the x² term and the wrong number under the square root.
3. **2x√15x**: This could also be incorrect due to the form of x.
4. **30x³**: This is incorrect, as it's just a cubic term.
None of the provided responses seem to accurately transform the original expression \( 60\sqrt[3]{x} \). However, it appears that there may be a misunderstanding of how we should approach the simplification or interpretation of what's being asked.
Based on common sense and the multiple approaches above, please double-check the responses or reanalyze the question.
Until you find a response that matches what was simplified, it's possible none might be accurate, so verifying them against the derived expectations above could be key in understanding the simplification steps.