Question

use the calculator below to approximate \\(\sqrt{83}\\) as a decimal to the tenths place. note that you must do the approximation without using a square root button. your answer must be within a tenth of the actual value. \\(\sqrt{83} \approx \square\\)

Explanation:

Step1: Identify perfect squares around 83

We know that \(9^2 = 81\) and \(10^2 = 100\). So \(\sqrt{83}\) is between 9 and 10.

Step2: Check the tenths place

Let's try \(9.1^2=9.1\times9.1 = 82.81\) and \(9.2^2 = 9.2\times9.2=84.64\). Since \(82.81<83<84.64\), \(\sqrt{83}\) is between 9.1 and 9.2. Now, \(83 - 82.81 = 0.19\) and \(84.64 - 83 = 1.64\). Since 0.19 is much closer to 0 than 1.64 is, \(\sqrt{83}\approx9.1\) (to the tenths place).

Answer:

\(9.1\)