Chapter 4.6, Problem 5GP

To determine

To find:the square root to the nearest integer.

Answer to Problem 5GP

Thesquare root to the nearest integeris $-7$ .

Explanation of Solution

Given information :

The expression is $-\sqrt{48}$

Calculation :

The first perfect square less than 48 is 36

The first perfect square greater than 48 is 49.

  $\begin{array}{l}36<48<49\\ 6^2<48<7^2\\ \sqrt{6^2}<48<\sqrt{7^2}\\ 6<\sqrt{48}<7\end{array}$

The square root of 48 is between the integers $-6$ and $-7$ .Since 48 is closer to 49 than to 36.

Hence, $-7$ is nearest integer square root to the expression $-\sqrt{48}$ .