Question
the square root of 56 is between which two numbers The choices are 8 and 8.5 7 and 7.5 6.5 and 7 7.5 and 8
Answers
GPT-4o mini
To find the square root of 56, we can estimate it by determining the squares of whole numbers around it.
- \(7^2 = 49\)
- \(8^2 = 64\)
Since 56 is between 49 and 64, we know that:
\[
7 < \sqrt{56} < 8
\]
To further narrow it down, we can check \(7.5^2\):
\[
7.5^2 = 56.25
\]
Since \(56 < 56.25\), we confirm that:
\[
\sqrt{56} < 7.5
\]
Thus, we can conclude that \( \sqrt{56} \) is between \( 7 \) and \( 7.5 \).
Therefore, the correct choice is **6.5 and 7**.
- \(7^2 = 49\)
- \(8^2 = 64\)
Since 56 is between 49 and 64, we know that:
\[
7 < \sqrt{56} < 8
\]
To further narrow it down, we can check \(7.5^2\):
\[
7.5^2 = 56.25
\]
Since \(56 < 56.25\), we confirm that:
\[
\sqrt{56} < 7.5
\]
Thus, we can conclude that \( \sqrt{56} \) is between \( 7 \) and \( 7.5 \).
Therefore, the correct choice is **6.5 and 7**.