Alright, let's go step-by-step to solve the problem of estimating the value of [tex]\(\sqrt{97.5} \div 1.96\)[/tex].
1. First, we need to find the square root of 97.5. Doing this will give us the intermediate value we need before we proceed to the division.
[tex]\[
\sqrt{97.5} \approx 9.8742
\][/tex]
2. Next, we need to divide this result by 1.96. We already have the square root calculated, so the final step is straightforward:
[tex]\[
\frac{9.8742}{1.96} \approx 5.0379
\][/tex]
So, the estimated value of [tex]\(\sqrt{97.5} \div 1.96\)[/tex] is approximately [tex]\( 5.0379 \)[/tex].
