To evaluate Sandra's simplification of \( 45 - \sqrt{23} \), let's simplify the expression correctly to see if she made an error.
We need to clarify what \( 45 - \sqrt{23} \) means. Assuming she meant \( 45 - \sqrt{23} \):
- Check for simplification of \( \sqrt{23} \): The square root of 23 cannot be simplified further because 23 is a prime number.
- Combine the radicals: If there were any radicals to combine, we would look for like terms. However, we only have one radical, \( \sqrt{23} \).
From what we see, Sandra ended up with \( \sqrt{815} \), which could mean she incorrectly combined or translated components from the original expression.
Let's look at the claims from the responses:
- Sandra's answer is not correct. She could continue to simplify the radical to get \( \sqrt{245} \): This is incorrect; we cannot simplify \( \sqrt{23} \) to \( \sqrt{245} \).
- Sandra's answer is not correct. She could continue to simplify the radical to get \( 24 \sqrt{5}: Incorrect; there is no ( 24 \sqrt{5} \) from \( 45 - \sqrt{23} \).
- Sandra's simplified answer is correct.: This seems at first glance to be questionable since there is no evident simplification that leads directly to \( \sqrt{815} \) without more context.
- Sandra's answer is not correct. She should have added the coefficients to get ( 6\sqrt{15}: Not applicable since there's no additional radical to combine.
- Sandra's answer is not correct. She should have multiplied \( 4 \times 5 \) in the first radical and multiplied \( 2 \times 3 \) in the second radical to get a final answer of \( 26: This is incorrect as there are no such multiplicative components visible in the expression ( 45 - \sqrt{23} \).
Since none of the options seem accurate based on typical simplification processes of radicals, it's likely Sandra's answer of \( \sqrt{815} \) isn't yielding a simplifiable form derived from \( 45 - \sqrt{23} \) correctly.
Thus, the overall conclusion is: Sandra's answer is not correct. The formatting of her final answer appears flawed without clear reasoning from the provided expression \( 45 - \sqrt{23} \). More context would be needed for direct verification or consolidation of terms in her original submission.
1 answer