Table of Contents
- Square Root Approximation
- What’s Next?
In the previous segment, we used the long division method to find the square root of a number. In this segment, we will learn about approximating square roots.
How to find the approximate value of square root of a number?
All numbers are not perfect squares and sometimes it may not be possible to indulge in extensive calculations to find the square roots of a number. In such situations, the best way to find the square roots is by approximation.
Let us understand how to find the approximate square roots with some examples.
Q. Find the square root of 55. Solution:
Step 1: Find two perfect squares between which 55 lies. 55 lies between 49 and 64, which are perfect squares.
72 = 49???82 = 64.
Thus, the square root of 55 lies between 7 and 8.
Step 2: Find out how far 55 is from 49, relative to how far 64 is from 49.
For this, first find the difference between the perfect squares, 64 and 49, and then the difference between 55 and 49.
64 – 49 = 15
55 – 49 = 6
6 will tell us how far the answer is from 7.
15
6 2
=
15 5
=0.4
So, the √55is approximately equal to 7.4.
