Question

approximate \\(\sqrt{97}\\) by following the steps below.\\(\sqrt{97}\\) must lie between the whole numbers \\(\square\\) and \\(\square\\)

Explanation:

Step1: Find perfect squares around 97

We know that \(9^2 = 81\) and \(10^2=100\).

Step2: Compare with 97

Since \(81<97<100\), taking square roots (and since square root is an increasing function), we have \(\sqrt{81}<\sqrt{97}<\sqrt{100}\), which simplifies to \(9 < \sqrt{97}< 10\).

Answer:

9 and 10