Question

Approximate square root of, 91, end square root
91
​

square root of, 91, end square root
91
​
must lie between the whole numbers
9
9 and
10
10 because 9, squared, equals, start box, 81, end box9
2
=
81
​
and 10, squared, equals, start box, 100, end box10
2
=
100
​
, and 91 lies between these values.
Drag square root of, 91, end square root
91
​
based on your estimate above:
Real
√91
__
_
To one decimal place, square root of, 91, end square root
91
​
must lie between
9.5
9.5 and
9.6
9.6 because 9, point, 5, squared, equals, start box, 90, point, 2, 5, end box9.5
2
=
90.25
​
and 9, point, 6, squared, equals, start box, 92, point, 1, 6, end box9.6
2
=
92.16
​
, and 91 lies between these values.
Drag square root of, 91, end square root
91
​
based on your estimate above:
Real
√91
__
_
To two decimal places, square root of, 91, end square root
91
​
must lie between
and

Answer 1

To find the square root of 91 with increasing precision:

1. **Whole Numbers**: As you've noted, \(\sqrt{91}\) lies between 9 and 10.
- \(9^2 = 81\)
- \(10^2 = 100\)

2. **To One Decimal Place**: \(\sqrt{91}\) must lie between 9.5 and 9.6.
- \(9.5^2 = 90.25\)
- \(9.6^2 = 92.16\)

3. **To Two Decimal Places**:
- To narrow it down further, we need to check the values between 9.5 and 9.6.
- Let's check 9.54 and 9.55:
- \(9.54^2 = 91.0516\) (greater than 91)
- \(9.53^2 = 90.2409\) (less than 91)
- Thus, \(\sqrt{91}\) lies between 9.53 and 9.54.

Therefore, to summarize, we have:
- **To two decimal places**, \(\sqrt{91}\) must lie between **9.53** and **9.54**.