Chapter 4.6, Problem 25IP

To determine

To find:the square root to the nearest integer.

Answer to Problem 25IP

Thesquare root to the nearest integeris $-4$ .

Explanation of Solution

Given information :

The expression is $-\sqrt{14}$

Calculation :

The first perfect square less than 14 is 9

The first perfect square greater than 14is 16.

  $\begin{array}{l}9<14<16\\ 3^2<14<4^2\\ \sqrt{3^2}<14<\sqrt{4^2}\\ 3<\sqrt{14}<4\end{array}$

The square root of 14 is between the integers $-3$ and $-4$ .Since 14 is closer to 16 than to 9.

Hence, $-4$ is nearest integer square root to the expression $-\sqrt{102}$ .