Question

approximate \\(\sqrt{82}\\) by following the steps below. \\(\sqrt{82}\\) must lie between the whole numbers \\(\square\\) and \\(\square\\)

Explanation:

Step1: Find perfect squares around 82

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

Step2: Compare with \(\sqrt{82}\)

Since \(81<82<100\), taking square roots (and noting that square root is an increasing function), we get \(\sqrt{81}<\sqrt{82}<\sqrt{100}\), which simplifies to \(9 < \sqrt{82}< 10\).

Answer:

9 and 10