Chapter 9.2, Problem 45E

To determine

Find the approximate square root to the nearest integer.

Answer to Problem 45E

The square root to the nearest integer is $10$ .

Explanation of Solution

Given:

It is given in the question that the root is $\sqrt{103}$ .

Concept Used:

In this, use the concept of identify two perfect squares closest to the given number.One before the number and one after.

Calculation:

Here, the root is $\sqrt{103}$ .

Now, find the two perfect squares closest to the number which is

  ${10}^2=100<103<121={11}^2$

Hence, the square root of $103$ is somehow between $10$ and $11$ . Since the given number is much closer to ${10}^2=100$ than $121={11}^2$ ,so it can be deduce that the closest integer to the square root is $10$ .

Conclusion:

The square root is $10$ .