Chapter 9.7, Problem 40CCR

To determine

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

Answer to Problem 40CCR

The best integer estimate for $\sqrt{98}$ is $10$ .

Explanation of Solution

Given information :

The given expression:

  $\sqrt{98}$

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:

  $\sqrt{98}$

The largest perfect square less than $98$ is $81$ . [ $\sqrt{81}=9$ ]

The smallest perfect square greater than $98$ is $100$ . [ $\sqrt{100}=10$ ]

Plot each square root on a number line. Then estimate $\sqrt{98}$ .

  $\begin{array}{l}81<98<100\text{ [Write an inequality]}\\ 9^2<98<{10}^2\text{ [81}=9^2\text{ and }100={10}^2]\\ \sqrt{9^2}<\sqrt{98}<\sqrt{{10}^2}\text{ [Find the square root of each number}]\\ 9<\sqrt{98}<10\text{ [Simplify}]\end{array}$

So, $\sqrt{98}$ is between $9$ and $10$ . Since $98$ is closer to $100$ than to $81$ , the best integer estimate for $\sqrt{98}$ is $10$ .