56−−√

is between what two numbers?(1 point)
Responses

7.5 and 8
7.5 and 8

7 and 7.5
7 and 7.5

8 and 8.5
8 and 8.5

6.5 and 7

1 answer

To find the square root of 56 (√56) and determine between which two numbers it falls, we can estimate:

  1. 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:

\[ 7 < \sqrt{56} < 8 \]

  1. 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.