To verify Sandra's simplification of \( 45 - \sqrt{23} \), let's break it down step by step.
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Understanding what \( 45 - \sqrt{23} \) means: This expression contains a whole number (45) and a radical part (\(-\sqrt{23}\)).
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Sandra's claim: Sandra simplified it to \( \sqrt{815} \).
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Examine if \( 45 - \sqrt{23} \) can be expressed as \( \sqrt{815} \):
- \( \sqrt{815} \) can be simplified further:
- \( 815 = 5 \times 163 \)
- Thus, \( \sqrt{815} \) could be left in that form as \( \sqrt{5 \times 163} \) but we are interested in checking if it can be represented as \( 45 - \sqrt{23} \).
- \( \sqrt{815} \) can be simplified further:
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Conclusion about Sandra's answer:
- \( 45 - \sqrt{23} \) is a numerical expression that does not equal \( \sqrt{815} \).
- Therefore, Sandra's answer is not correct, as these two expressions are not equivalent.
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Identifying the mistake:
- It appears that Sandra likely misunderstood how to simplify the expression correctly. Since it looks like she tried to combine terms improperly or misinterpret the operation with radicals.
Based on these observations, the correct choice would be: "Sandra's answer is not correct. She could continue to simplify the radical to get \( 24 \sqrt{5} \)." However, if that doesn’t fit valid choices, the best response might point out the nature of \( 45 \) and \( \sqrt{23} \) being separate terms that do not combine.
If you'd like a more specific answer from the options provided that seemed to allude to a miscalculation, the correct response could be: "Sandra's answer is not correct. She should have added the coefficients to get \( 6\sqrt{15} \)."
It is important to clarify the context, as the exact answer may vary without constraints on what \( 45 - \sqrt{23} \) could resolve into directly related novel expressions.
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