Question
384−−−√3 (1 point) Responses 46–√3 4 cube root of 6 86–√3 8 cube root of 6 68–√3 6 cube root of 8 64–√3
Answers
GPT-4o mini
To simplify the expression \( \sqrt{384 - 3} \), we first calculate \( 384 - 3 \):
\[
384 - 3 = 381
\]
Now we take the square root of 381:
\[
\sqrt{381}
\]
Next, we need to find the approximate value of \( \sqrt{381} \). The closest perfect squares are \( 361 (19^2) \) and \( 400 (20^2) \), indicating that \( 19 < \sqrt{381} < 20 \).
However, we do not see a direct match with the provided options.
The responses are:
1. \( 46 - \sqrt{3} \)
2. \( 4 \cdot \sqrt[3]{6} \)
3. \( 86 - \sqrt{3} \)
4. \( 8 \cdot \sqrt[3]{6} \)
5. \( 68 - \sqrt{3} \)
6. \( 6 \cdot \sqrt[3]{8} \)
7. \( 64 - \sqrt{3} \)
Since none of these options appear to match \( \sqrt{381} \) at this point, it seems there might have been some confusion or additional context needed to correlate the square root simplifications with the specific choices given. If you mean something different contextually or the expression was phrased differently, could you clarify the starting expression?
\[
384 - 3 = 381
\]
Now we take the square root of 381:
\[
\sqrt{381}
\]
Next, we need to find the approximate value of \( \sqrt{381} \). The closest perfect squares are \( 361 (19^2) \) and \( 400 (20^2) \), indicating that \( 19 < \sqrt{381} < 20 \).
However, we do not see a direct match with the provided options.
The responses are:
1. \( 46 - \sqrt{3} \)
2. \( 4 \cdot \sqrt[3]{6} \)
3. \( 86 - \sqrt{3} \)
4. \( 8 \cdot \sqrt[3]{6} \)
5. \( 68 - \sqrt{3} \)
6. \( 6 \cdot \sqrt[3]{8} \)
7. \( 64 - \sqrt{3} \)
Since none of these options appear to match \( \sqrt{381} \) at this point, it seems there might have been some confusion or additional context needed to correlate the square root simplifications with the specific choices given. If you mean something different contextually or the expression was phrased differently, could you clarify the starting expression?