An irrational number, d , has a value such that 6 < d < 7 . Which of the following is a possible value for d?

A. /6.2

B. 2π

C. /13

D. 6π

1 answer

To determine which option could be a possible value for the irrational number \( d \) that satisfies \( 6 < d < 7 \), let's evaluate each of the given options:

A. \( \sqrt{6.2} \)

Calculating \( \sqrt{6.2} \):

  • \( \sqrt{6.2} \approx 2.49 \), which is not within the range \( 6 < d < 7 \).

B. \( 2\pi \)

Calculating \( 2\pi \):

  • \( 2\pi \approx 6.283 \), which is within the range \( 6 < d < 7 \) and is an irrational number.

C. \( \sqrt{13} \)

Calculating \( \sqrt{13} \):

  • \( \sqrt{13} \approx 3.61 \), which is not within the range \( 6 < d < 7 \).

D. \( 6\pi \)

Calculating \( 6\pi \):

  • \( 6\pi \approx 18.85 \), which is not within the range \( 6 < d < 7 \).

Among the options, the only one that is both an irrational number and falls within the range \( 6 < d < 7 \) is:

B. \( 2\pi \).