Chapter 9.7, Problem 39CCR

To determine

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

Answer to Problem 39CCR

The best integer estimate for $\sqrt{80}$ is $9$ .

Explanation of Solution

Given information :

The given expression:

  $\sqrt{80}$

Concept used:

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

Calculation :

As per problem,

The given square root:

  $\sqrt{80}$

The largest perfect square less than $80$ is $64$ . [ $\sqrt{64}=8$ ]

The smallest perfect square greater than $80$ is $81$ . [ $\sqrt{81}=9$ ]

Plot each square root on a number line. Then estimate $\sqrt{80}$ .

  $\begin{array}{l}64<80<81\text{ [Write an inequality]}\\ {\text{8}}^2<80<9^2\text{ [64}={\text{8}}^2\text{ and }81=9^2]\\ \sqrt{{\text{8}}^2}<\sqrt{80}<\sqrt{9^2}\text{ [Find the square root of each number}]\\ 8<\sqrt{80}<9\text{ [Simplify}]\end{array}$

So, $\sqrt{80}$ is between $8$ and $9$ . Since $80$ is closer to $81$ than to $64$ , the best integer estimate for $\sqrt{80}$ is $9$ .