Chapter 9.7, Problem 44CCR

To determine

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

Answer to Problem 44CCR

The best integer estimate for $-\sqrt{198}$ is $-14$ .

Explanation of Solution

Given information :

The given expression:

  $-\sqrt{198}$

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:

  $-\sqrt{198}$

The largest perfect square less than $198$ is $196$ . [ $\sqrt{196}=14$ ]

The smallest perfect square greater than $198$ is $225$ . [ $\sqrt{225}=15$ ]

The negative square root of $198$ is between the integers $-14$ and $-15$ . Plot each square root on a number line. Then estimate $-\sqrt{198}$ .

So, $-\sqrt{198}$ is between $-15$ and $-14$ . Since $198$ is closer to $196$ than to $225$ , the best integer estimate for $-\sqrt{198}$ is $-14$ .