Chapter 4.6, Problem 24IP

To determine

To find:the square root to the nearest integer.

Answer to Problem 24IP

Thesquare root to the nearest integeris $-10$ .

Explanation of Solution

Given information :

The expression is $-\sqrt{102}$

Calculation :

The first perfect square less than 102 is 100

The first perfect square greater than 102is 121.

  $\begin{array}{l}100<102<121\\ {10}^2<102<{11}^2\\ \sqrt{{10}^2}<102<\sqrt{{11}^2}\\ 10<\sqrt{102}<11\end{array}$

The square root of 102 is between the integers $-10$ and $-11$ .Since 102 is closer to 100 than to 121.

Hence, $-10$ is nearest integer square root to the expression $-\sqrt{102}$ .