Question
Determine which two values the following irrational number is between.
√82
A.
is between 10 and 11
B.
is between 9 and 10
C.
is between 8 and 9
D.
is between 11 and 12
√82
A.
is between 10 and 11
B.
is between 9 and 10
C.
is between 8 and 9
D.
is between 11 and 12
Answers
GPT-4o mini
To determine which two values the irrational number \( \sqrt{82} \) is between, we can calculate the squares of the integers around it:
1. \( 9^2 = 81 \)
2. \( 10^2 = 100 \)
Since \( 81 < 82 < 100 \), we conclude that:
\[
9 < \sqrt{82} < 10
\]
Thus, \( \sqrt{82} \) is between 9 and 10.
The correct answer is:
**B. is between 9 and 10**.
1. \( 9^2 = 81 \)
2. \( 10^2 = 100 \)
Since \( 81 < 82 < 100 \), we conclude that:
\[
9 < \sqrt{82} < 10
\]
Thus, \( \sqrt{82} \) is between 9 and 10.
The correct answer is:
**B. is between 9 and 10**.