Question

Approximate square root of, 96, end square root
96
​

square root of, 96, end square root
96
​
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 96 lies between these values.
Drag square root of, 96, end square root
96
​
based on your estimate above:
Real
√96
__
_
To one decimal place, square root of, 96, end square root
96
​
must lie between
and

Answer 1

To find the approximate square root of \( \sqrt{96} \), we can start by using the information you provided, where \( 9^2 = 81 \) and \( 10^2 = 100 \). Since \( 96 \) lies between \( 81 \) and \( 100 \), we can conclude that:

\[
9 < \sqrt{96} < 10
\]

To refine our estimate further, we can calculate \( 9.5^2 \):

\[
9.5^2 = 90.25
\]

Since \( 90.25 < 96 \), we know that \( \sqrt{96} > 9.5 \).

Next, we can calculate \( 9.8^2 \):

\[
9.8^2 = 96.04
\]

Since \( 96.04 > 96 \), we know that \( \sqrt{96} < 9.8 \).

Now we have:

\[
9.5 < \sqrt{96} < 9.8
\]

For a closer approximation, we can check \( 9.7^2 \):

\[
9.7^2 = 94.09
\]

Since \( 94.09 < 96 \), we know that \( \sqrt{96} > 9.7 \).

Putting this all together, we can refine our approximation further:

\[
9.7 < \sqrt{96} < 9.8
\]

Thus, to one decimal place, \( \sqrt{96} \) must lie between \( 9.7 \) and \( 9.8 \).