How to find Square Root of Large Numbers Quickly without Calculator

Author: Anil kumar (M.Tech.) Former Lecturer

Here you can learn a trick to find the square root of Large numbers through which you will be able to solve these type of questions quickly without calculator. These numbers have to be perfect squares and not in decimals. The traditional method of finding square root of numbers takes a lot of time. But through this trick we can solve these types of questions easily in seconds. So check the trick given here so that you can solve square root of numbers which are perfect squares.

Shortcut Trick on How to find Square Root of Large Numbers Quickly in Seconds without calculator

First you need to memorize the below given table which will be helpful in solving square root questions.
Number
Square
Last digit of Square
0
0
0
1
1
1
2
4
4
3
9
9
4
16
6
5
25
5
6
36
6
7
49
9
8
64
4
9
81
1

Now we will learn through examples to find the Square root of a number:

Suppose square root of 2025 is to be determined.
Create a sets of two numbers i.e. a pair from right side. For a 3 digit number, then we can make two sets of one digit and two digit.

For example 225 can be divided in two sets as 25 and 2. Similarly 2025 can be divided into 20 and 25. Similarly 11025 can be divided into 110 and 25.

We will understand it with an example.
Example 1.
Find square root of 2025.
Solution:
1: First make pairs from right. So ignore last two digits of 2025 i.e. 25. The remaining number is ’20′.
2: Now from the above table (in 1st column from left side), find square of a number which is less than and nearest to 20. That number is 4. So ’4′ will be our left part of answer.
3: Now last two digits of  ’2025‘ is ‘25‘. The last digit of 25 is 5. So check 3rd table from left. You will find 5 only once. Now look corresponding number to this 5 in 1st column from left which is 5. Therefore right part (R) of our answer will be ’5′.
4: Our Answer will be X|Y (X is left part while Y is right part of answer). Therefore Answer will be 45.
So square root of √2025 = 45

Example 2:
Find the square root of 3249.
Solution:
1: Now ignore last two digits of 3249 i.e. 49. Remaining number is ’32′.
2: From above table, find square of a number which is less than and nearest to 32. That number is 5 which is our left part answer (X). 
3: Since last digit of  ’3249‘ is ‘9‘. Check 3rd column from left. You will find 9 two times. Now look corresponding number to this 9 in 1st column. You can find 3 & 7. So right part of answer will be among this 3 or 7. Now we have to find whether it is 3 or 7. For that, multiply left part answer with its next number i.e. 5*6 which comes out to be 30. This 30 is less than 32. It means right part answer will be bigger of 3 or 7 which is 7 (Y).
Step 4: Our Answer will be X|Y. Therefore Answer will be 57.
Note: if the multiplication of left part answer multiplied by (left part answer+1) in this question comes to be greater than 32 in this question, then the right part answer will be smaller of 3 or 7. It means 3.

Example 3:
Find the square root of 24336.
Solution:
1: Make pairs from right side of 24336. Since it is a 5 digit number. So right pair will be 36 and left pair will be 243. We first calculate this 243.
2: Now find square of a number which is less than and nearest to 243. That number will be 15. So left part of answer will be ’15′. Let it be X.
3: Since last digit of  24336 is 6. Check 6 in last digit to square column. Now look corresponding to the number in 1st column. 6 comes two times. You will find 4 and 6. So right part of answer can be either 4 or 6. Now we have to find whether it is 4 or 6. For that, multiply left part answer with 1 added in it means multiply 15 with next number 16.
So 15*16 = 240 which is less than 243 (always compare with left part). It means right part answer will be bigger of 4 or 6 which is 6.
4: Our Answer will be X|Y. So Answer will be 156 = 156.

So this is the trick on how to find Square root of Large numbers quickly without calculator.