To determine which of the options is a rational number between 8 and 18, let’s evaluate each option:
A. √75
- Calculating √75 gives approximately 8.66 (since √75 ≈ 8.66).
- This is between 8 and 18, but we need to check if it's rational. The square root of 75 simplifies to \( 5\sqrt{3} \), which is irrational.
B. 8 3/5
- Converting this mixed number to an improper fraction: \( 8 + \frac{3}{5} = \frac{40}{5} + \frac{3}{5} = \frac{43}{5} = 8.6 \).
- This is between 8 and 18 and is rational.
C. 8 1/3
- Converting this mixed number to an improper fraction: \( 8 + \frac{1}{3} = \frac{24}{3} + \frac{1}{3} = \frac{25}{3} \approx 8.33 \).
- This is between 8 and 18 and is rational.
D. √74
- Calculating √74 gives approximately 8.6 (since √74 ≈ 8.6).
- This is also between 8 and 18, but as with option A, √74 is irrational.
From the above evaluations:
- Options B and C are both rational numbers between 8 and 18.
Therefore, the correct answers are: B. 8 3/5 C. 8 1/3
If you need just one answer to fit the question, you can select either B or C.
20 answers