Question

approximate \\(\sqrt{53}\\) by following the steps below.\\(\sqrt{53}\\) must lie between the whole numbers 7 and 8 because \\(7^2 = 49\\) and \\(8^2 = 64\\), and 53 lies between these values. drag \\(\sqrt{53}\\) based on your estimate above: to one decimal place, \\(\sqrt{53}\\) must lie between \\(\square\\) and \\(\square\\)

Explanation:

Step1: Calculate \(7.2^2\)

We know that to find the range to one decimal place, we start by squaring numbers with one decimal place around 7 and 8. First, calculate \(7.2^2\).
\(7.2^2 = 7.2\times7.2 = 51.84\)

Step2: Calculate \(7.3^2\)

Next, calculate \(7.3^2\).
\(7.3^2 = 7.3\times7.3 = 53.29\)

Step3: Compare with 53

We know that \(51.84<53<53.29\), which means \(\sqrt{51.84}<\sqrt{53}<\sqrt{53.29}\), and since \(\sqrt{51.84} = 7.2\) and \(\sqrt{53.29}=7.3\), so \(\sqrt{53}\) lies between 7.2 and 7.3.

Answer:

To one decimal place, \(\sqrt{53}\) must lie between \(7.2\) and \(7.3\)