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HOW TO QUICKLY FIND SQUARE ROOT OF LARGE NUMBERS QUICKLY IN SECONDS MENTALLY

Here is the trick to find the square root of those numbers which are perfect squares only quickly. For solving square roots of perfect square numbers we don’t need to solve them through traditional method of solving. Instead we can solve them mentally by using tricks. So here is the trick which will let you solve square root of numbers which are perfect squares.
For calculating the square root of numbers,
you need to learn the below given table as it will let you solve square root questions quickly.
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

We will follow the steps given in below examples to find the Square root of a number:

Suppose we want to find the square root of 2025.
To solve this type of questions, we creates multiple sets of the given number taking two at a time starting from right. If it is a three digit number, then we make two sets as
First-The last two numbers
Second-the remaining number.

For example 256 can be divided in two sets as 56 and 2.
If we make sets of four digit numbers. Then it will be 2 sets starting from left. For example: 2025 can be divided into 20 and 25.

Below is an example.
Example 1.
Find square root of 2025.
Solution:
Step 1: First we need to ignore last two digits of 2025. So ignore 25. The number remaining is ’20′.
Step 2: Now from the above table, try to find square of a number which is less than and nearest to 20. That number is 4. So left part of our answer will be ’4′.
Step 3: Since last digit of  ’2025‘ is ‘5‘. Therefore right part (R) of our answer will be ’5′.
Step 4: Our Answer will be X|Y. Therefore Answer will be 4|5 = 45.

So the square root of √2025 = 45
Example 2:
Find the square root of 3249.
Solution:
Step 1: First we need to ignore last two digits of 3249. So ignore 49. The number remaining is ’32′.
Step 2: Now from the above table, try to find square of a number which is less than and nearest to 32. That number is 5. So left part of answer will be ’5′.
Step 3: Since last digit of  ’3249‘ is ‘9‘. So right part of answer will be 3 or 7. Now we have to find whether it is 3 or 7. For that, multiply left part answer with 1 added in it means multiply 5 with 6. 5*6 = 30 which is less than 32. It means right part answer will be bigger of 3 or 7 which is 7.
Step 4: Our Answer will be X|Y. Therefore Answer will be 5|7 = 57.
Note: if the multiplication of left part answer*(left part answer+1) comes to be greater than left part of question given number, then the right part answer will be smaller of the [last digit to square].
Example 3:
Find the square root of 24336.
Solution:
Step 1: First we need to ignore last two digits of 24336. So ignore 36. So the number remaining is ’243′.
Step 2: Now from the above table, find square of a number which is less than and nearest to 243. That number is 15. So left part of answer will be ’15′.
Step 3: Since last digit of  24336 is 6. So from the table given above, find 6 in last digit to square column.  There are two 6 given in last digit to square column. And the numbers given corresponding to 6 under number column are 4 and 6. So right part of answer will be 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 16. 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.

Step 4: Our Answer will be X|Y. Therefore Answer will be 15|6 = 156.

13 comments:

  1. Great site Anil..... Keep this good work going...... Thank you.....

    ReplyDelete
  2. thank u anil its just superb.. i have a doubt ie.,

    how to fiind out the square root of the nos like......60918 ,, or the nos ending with ,2,3,7,8 plz reply waitin here

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
    2. This method applicable only on perfect squares root...i.e no. Ending with 1,4,5,6,9

      Delete
  3. Dear sharath, you have to find out the square root of 60918 by normal method. this trick is for numbers which are perfect square. 60918 is not a perfect square.

    ReplyDelete
  4. Sir,how to find square root for six dogits numbers ?

    ReplyDelete
  5. how to find out the square root of 289 ?

    ReplyDelete

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