Chapter 9.2, Problem 43E

To determine

Find the approximate square root to the nearest integer.

Answer to Problem 43E

The square root to the nearest integer is $7$ .

Explanation of Solution

Given:

It is given in the question that the root is $\sqrt{47}$ .

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 $\sqrt{47}$ .

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

  $6^2=36<47<49=7^2$

Hence, the square root of $47$ is somehow between $6$ and $7$ . Since the given number is much closer to $49=7^2$ than $6^2=36$ ,so it can be deduce that the closest integer to the square root is $7$ .

Conclusion:

The square root is $7$ .