To determine whether Sandra is correct or not, let's simplify the expression \( 45 - \sqrt{23} \).
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Step 1: Interpret the expression.
- It seems like there is confusion because it's not clear whether Sandra tried to simplify \( 45 - \sqrt{23} \) or \( \sqrt{45} - \sqrt{23} \). Let's assume she meant the latter since the other expression doesn't seem to simplify to a square root.
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Step 2: Simplifying \( \sqrt{45} - \sqrt{23} \).
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We start by simplifying \( \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]
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Thus, the expression becomes: \[ 3\sqrt{5} - \sqrt{23} \]
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Step 3: Analyzing Sandra's answer.
- Sandra ended up with \( \sqrt{815} \). This does not match our simplification of \( 3\sqrt{5} - \sqrt{23} \).
- Her answer seems to be a simplification that is incorrect when comparing to the basic operations on square roots.
Given this reasoning, Sandra's answer is indeed not correct. The closest response to her mistake is:
- Sandra's answer is not correct. She should have added the coefficients to get \( 6\sqrt{15} \).
This indicates she's potentially miscalculating or misapplying the properties of square roots. However, instead of adding coefficients, which is incorrect, the actual simplification did not involve addition. Therefore, the first part of that response needs revision for accuracy.
Ultimately, a more accurate response would say:
Sandra's answer is not correct. She should have simplified \( \sqrt{45} \) as \( 3\sqrt{5} \) and left \( \sqrt{23} \) unchanged, thus obtaining \( 3\sqrt{5} - \sqrt{23} \).