Question

Find the square root of 96

Answer 1

To find the square root of 96, we can simplify it first.

1. Begin by factorizing 96:
\[
96 = 16 \times 6 = 16 \times (3 \times 2)
\]
Thus, we can express 96 as:
\[
96 = 16 \times 6
\]

2. The number 16 is a perfect square:
\[
16 = 4^2
\]
Therefore, we can rewrite the square root of 96 as:
\[
\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
\]

To find a numerical approximation for \(\sqrt{96}\):
- Calculate \( \sqrt{6} \) which is approximately 2.449.
- Thus:
\[
4\sqrt{6} \approx 4 \times 2.449 \approx 9.796
\]

So, the square root of 96 is:
\[
\sqrt{96} = 4\sqrt{6} \approx 9.798
\]

In conclusion, the square root of 96 can be expressed as \( 4\sqrt{6} \) or approximately \( 9.798 \).