Question

Approximate square root of, 56, end square root
56
​

square root of, 56, end square root
56
​
must lie between the whole numbers
7
7 and
8
8 because 7, squared, equals, start box, 49, end box7
2
=
49
​
and 8, squared, equals, start box, 64, end box8
2
=
64
​
, and 56 lies between these values.
Drag square root of, 56, end square root
56
​
based on your estimate above:
Real
√56
__
_
To one decimal place, square root of, 56, end square root
56
​
must lie between
7.4
7.4 and
7.5
7.5 because 7, point, 4, squared, equals, start box, 54, point, 7, 6, end box7.4
2
=
54.76
​
and 7, point, 5, squared, equals, start box, 56, point, 2, 5, end box7.5
2
=
56.25
​
, and 56 lies between these values.
Drag square root of, 56, end square root
56
​
based on your estimate above:
Real
√56
__
_
To two decimal places, square root of, 56, end square root
56
​
must lie between
and

Answer 1

To estimate the square root of 56 to two decimal places, we can use the values we previously calculated and narrow it down further.

We already established that:

- \(\sqrt{56}\) lies between \(7.4\) and \(7.5\):
- \(7.4^2 = 54.76\)
- \(7.5^2 = 56.25\)

Now let's refine the estimation further by testing a midpoint or closer values within \(7.4\) and \(7.5\):

1. **Try \(7.45\)**:
\[
7.45^2 = 55.9025 \quad (\text{which is} < 56)
\]

2. **Try \(7.48\)**:
\[
7.48^2 = 55.9004 \quad (\text{still} < 56)
\]

3. **Try \(7.49\)**:
\[
7.49^2 = 56.0001 \quad (\text{slightly} > 56)
\]

Since \(7.48^2\) is still less than 56 and \(7.49^2\) is slightly more than 56, we can conclude:

To two decimal places,
\[
\sqrt{56} \text{ lies between } 7.48 \text{ and } 7.49.
\]

### Final Answer
\[
\sqrt{56} \text{ lies between } 7.48 \text{ and } 7.49.
\]