Chapter 9.7, Problem 41CCR

To determine

To estimate : the given square root to the nearest integer.

Answer to Problem 41CCR

The best integer estimate for $\sqrt{48}$ is $7$ .

Explanation of Solution

Given information :

The given expression:

  $\sqrt{48}$

Concept used:

The square root of an integer that is not a perfect square is estimated by determining between which two consecutive integers the square lies.

Calculation :

As per problem,

The given square root:

  $\sqrt{48}$

The largest perfect square less than $48$ is $36$ . [ $\sqrt{36}=6$ ]

The smallest perfect square greater than $48$ is $49$ . [ $\sqrt{49}=7$ ]

Plot each square root on a number line. Then estimate $\sqrt{48}$ .

  $\begin{array}{l}36<48<49\text{ [Write an inequality]}\\ 6^2<48<7^2\text{ [36}=6^2\text{ and }49=7^2]\\ \sqrt{6^2}<\sqrt{48}<\sqrt{7^2}\text{ [Find the square root of each number}]\\ 6<\sqrt{48}<7\text{ [Simplify}]\end{array}$

So, $\sqrt{48}$ is between $6$ and $7$ . Since $48$ is closer to $49$ than to $36$ , the best integer estimate for $\sqrt{48}$ is $7$ .