Question
What integer is between \( \sqrt{3} \) and \( \frac{7 \pi}{8} ? \)
Ask by Watkins Romero. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The integer between \( \sqrt{3} \) and \( \frac{7\pi}{8} \) is 2.
Solution
1. We start by approximating the given expressions:
- \( \sqrt{3} \approx 1.732 \)
- \( \frac{7\pi}{8} \approx \frac{7 \times 3.1416}{8} \approx 2.75 \)
2. We are looking for an integer \( n \) such that:
\[
\sqrt{3} < n < \frac{7\pi}{8}
\]
Substituting the numerical approximations:
\[
1.732 < n < 2.75
\]
3. The only integer that satisfies this inequality is:
\[
n = 2
\]
Thus, the integer between \( \sqrt{3} \) and \( \frac{7\pi}{8} \) is \( 2 \).
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Simplify this solution Mind Expander
To find an integer between \( \sqrt{3} \) and \( \frac{7 \pi}{8} \), let's first approximate these values. The value of \( \sqrt{3} \) is approximately \( 1.732 \). Next, for \( \frac{7 \pi}{8} \), we first need to know that \( \pi \) is about \( 3.14 \). Thus, \( \frac{7 \pi}{8} \approx \frac{7 \times 3.14}{8} \approx \frac{21.98}{8} \approx 2.7475 \). Now we know: - \( \sqrt{3} \approx 1.732 \) - \( \frac{7 \pi}{8} \approx 2.7475 \) The integers between \( 1.732 \) and \( 2.7475 \) are \( 2 \). So the integer that lies between \( \sqrt{3} \) and \( \frac{7 \pi}{8} \) is \( 2 \).
