Chapter 9.7, Problem 42CCR

To determine

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

Answer to Problem 42CCR

The best integer estimate for $-\sqrt{35}$ is $-6$ .

Explanation of Solution

Given information :

The given expression:

  $-\sqrt{35}$

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:

  $-\sqrt{35}$

The largest perfect square less than $35$ is $25$ . [ $\sqrt{25}=5$ ]

The smallest perfect square greater than $35$ is $36$ . [ $\sqrt{36}=6$ ]

The negative square root of $35$ is between the integers $-5$ and $-6$ . Plot each square root on a number line. Then estimate $-\sqrt{35}$ .

So, $-\sqrt{35}$ is between $-6$ and $-5$ . Since $35$ is closer to $36$ than to $25$ , the best integer estimate for $-\sqrt{35}$ is $-6$ .