Question

Approximate square root of, 92, end square root
92
​

square root of, 92, end square root
92
​
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 92 lies between these values.
Drag square root of, 92, end square root
92
​
based on your estimate above:
Real
√92
__
_
To one decimal place, square root of, 92, end square root
92
​
must lie between
and

Answer 1

To estimate the square root of 92, we start with the perfect squares around 92, which you've already pointed out:

- \(9^2 = 81\)
- \(10^2 = 100\)

This means \( \sqrt{92} \) lies between 9 and 10.

To narrow it down further, we can try to find a more precise range:

- \(9.5^2 = 90.25\)
- \(9.6^2 = 92.16\)

Now we see that \( \sqrt{92} \) lies between \(9.5\) and \(9.6\) because \(90.25 < 92 < 92.16\).

So, to one decimal place, \( \sqrt{92} \) must lie between **9.5 and 9.6**.

You can drag it along the line as follows:

\[
\sqrt{92} \text{ is approximately between } 9.5 \text{ and } 9.6.
\]