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Ways to Find the Square Root of a Number – Unit Digits of Squares

The root of a number is an equal factor of the number.-

Table of contents

1. Square roots trick- Unit digit of squares

2. How to find square root of a four digit number

Firstly we need to learn the unit digits of all squares from 1 to 10 .

Square Numbers 1-10

 

As it is shown in the above table, whenever the unit digit of the square number is 9, the unit digit of the square root of that number will be definitely 3 or 7.

Furthermore, this rule can be applied to other numbers with the different unit digits.

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Let us take an example for this:


If the unit digit of a number is 6, then the unit digit of the square root of the number will be definitely 4 or 6.

How to find the square root of a Four digit number– Shortcuts

Finding the square root of a four digit number is very simple if we go through the below mentioned steps.

Let us take an example for this-: 
To Find the square root of 4489

First step-: We have to group the last pair of digits, and the rest of the digits together.

Now, check the  unit digit of 4489 which is 9 . So we can say that unit digit of its square root will be either 3 or 9.

Now we take only the first two digits  i.e. 44 . Since 44 comes in between the squares  of 6 and 7 (  62<44<72, please refer the above table for this), So we can definitely say that the ten’s digit of the square root of 4489 will be 6.
So far, we can say that the square root will be either 63 or 67.

Now, to find the exact unit digit, we consider the ten’s digit i.e. 6 and its successive digit, i.e, 7.

Multiply these two terms and we will get the following values :  

  6 x 7= 42 < 44                        

Since, 44 is greater than 42, the square root of 4489 will be larger of the two options i.e. 67.

So, the square root for 4489 will be 67.

This is a basic tactic to find the square root of a four digit number.

Let’s take another example to understand the procedure well:

Example:- Find the square root of  9801.

We will proceed step by step-:

First step:- We group the last pair of digits, and the rest of the digits together.

Now since the unit digits of 9801 is 1. So we can say that unit digit of its square root will be either 9 or 1 as in the following diagram.

 

Now we will cosider the first two digits i.e. 98. Since 98 comes in between the squares  of 9 and 10 , so we can say that the ten’s digits of the square root of 9801 will be 9, so far we can say that the square root will be either 91 or 99.

Now we will find the exact  unit digit.

To find the exact unit digit, we consider the ten’s digit i.e. 9 and the next number , i.e., 10 .

Multiplying both the numbers:

9 X 10 = 90 < 98

Since , 98 is greater than 90, so the square root of 9801 will be bigger of the two options i.e 99 .

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