Chapter 4.6, Problem 22IP

To determine

To find:the square root to the nearest integer.

Answer to Problem 22IP

Thesquare root to the nearest integeris $9$ .

Explanation of Solution

Given information :

The expression is $\sqrt{83}$

Calculation :

The first perfect square less than 83 is 81

The first perfect square greater than 83 is 100.

  $\begin{array}{l}81<83<100\\ 9^2<83<{10}^2\\ \sqrt{9^2}<83<\sqrt{{10}^2}\\ 9<\sqrt{83}<10\end{array}$

The square root of 83 is between the integers $9$ and $10$ .Since 83 is closer to 89 than to 100.

Hence, $9$ is nearest integer square root to the expression $\sqrt{83}$ .