Chapter 9.7, Problem 43CCR

To determine

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

Answer to Problem 43CCR

The best integer estimate for $\pm \sqrt{26}$ is $\pm 5$ .

Explanation of Solution

Given information :

The given expression:

  $\pm \sqrt{26}$

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:

  $\pm \sqrt{26}$

The square root will have two possible integers, one negative and one positive.

The largest perfect square less than $26$ is $25$ . [ $\sqrt{25}=5$ ]

The smallest perfect square greater than $26$ is $36$ . [ $\sqrt{36}=6$ ]

The positive square root of $26$ is between the integers $5$ and $6$ . Plot each square root on a number line. Then estimate $\sqrt{26}$ .

So, $\sqrt{26}$ is between $5$ and $6$ . Since $26$ is closer to $25$ than to $36$ , the best positive integer estimate for $\sqrt{26}$ is $5$ .

Now, the negative square root of $26$ is between the integers $-5$ and $-6$ . Plot each square root on a number line. Then estimate $-\sqrt{26}$ .

So, $-\sqrt{26}$ is between $-6$ and $-5$ . Since $26$ is closer to $25$ than to $36$ , the best negative integer estimate for $-\sqrt{26}$ is $-5$ .

Therefore, the best integer estimate for $\pm \sqrt{26}$ is $\pm 5$ .