TRICK: HOW TO FIND SQUARE ROOT OF LARGE NUMBERS QUICKLY IN MIND

Everyone try to search the quickest method to find the square root of large numbers.
So here is a method from which we can find the square root of perfect square easily.
Now it is not important to solve the square root from traditional methods that is commonly used in most of the exams.

You can use this mental trick in aptitude exams where calculator is not allowed like in campus exams and many government exams where these short tricks can save your time in a great extent.
So here is the trick lets workout.

For calculating the square root of a perfect square quickly you need to learn a small table given below :-

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

So now we will follow some steps to find the square root of a number with the help of an example.

Suppose we want to find the square root of number 2025.

To solve these type of questions, we will create multiple sets of given number taking two digits at a time starting from the right.

If there is a three digit number then we will make two sents as

First set - The last two numbers.

Second set- The remaining number.

Example - 256 can be divided in two sets as 56 and 2.

So for the digit 2025 we will make sets of four digit number with 2 sets starting from left.

Example - 2025 can be divided into 20 and 25 (two sets).

Example I

Lets find the square root of 2025.

SOLUTION:-

STEP-1 : First we need to ignore the last two digits of 2025. So ignore 25 and the remaining number is '20'.

STEP-2 : Now from the above table, try to find square of a number which is less than and nearest to 20. From table we found that number is 4.

So left part (L) 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.

Square root of √2025 is 45.

Example 2:

Find square root of 3249.

SOLUTION:-

STEP-1 : First ignore last two digits of 3249. So ignore 49.

The remaining number is '32'.

STEP-2 : Now from the above table, try to find the square of number which is less than and nearest to 32. That number is 5. So left part (L) of answer will be '5'.

STEP-3 : Since last digit of '3249' is 9. So from table we found that right part (R) of answer will be 3 or 7.

Now we have to find whether it is 3 or 7.For that multiply (L) left part answer and adding 1 in it. It means multiply 5 with (5+1) or  5x6 = 30 which is less than 32. It means right part answer will be bigger one of 3 or 7. So bigger 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 (last digit to square).

Example 3

Find 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. We found 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..