To find the square root of 56 (√56) and determine between which two numbers it falls, we can estimate:
- Calculate nearby perfect squares:
- \(7^2 = 49\)
- \(8^2 = 64\)
Since 49 is less than 56 and 64 is greater than 56, we can conclude that:
\[ 7 < \sqrt{56} < 8 \]
- Determine the approximate value of √56:
- We can further approximate \( \sqrt{56} \). It is equal to \( \sqrt{4 \times 14} = 2\sqrt{14} \).
- The approximate value of \( \sqrt{14} \) is about 3.74. Therefore: \[ 2 \times 3.74 \approx 7.48 \]
So \( \sqrt{56} \) is approximately 7.48, which is indeed between 7 and 7.5.
Thus, the correct response is:
7 and 7.5.