Aptitude: Easy Solution to find Square and Square root of a number

Square of numbers ending with 5

It’s simple logic, any multiplication of 5 will end with 25, so at end of the result it will be 25, in the result starting, it will be the multiplication of n * (n+1)

For Eg: 35 * 35

Where n = 3,

 3 * (3+1) = 3*4 = 12.

Append 25 to the result the answer is 1225

5 15 25

5 15 25

= = =

0 * (0+1) 25 1 * (1+1) 25 2 * (2+1) 25

25 225 625

Square of numbers ending with 1, 4, 6 and 9.

There is a small logic for this numbers ending.

For 1 and 6

26² = 25² + (25+26) = 625 + 51 = 676

71² = 70² + (70+71) = 4900 + 141 = 5041

For 4 and 9

24² = 25² – (25+24) = 625 – 49 = 576

69² = 70² - (70+69) = 4900 - 139 = 4761

Square root for four digit number.

First right out the squares from1 to 9.

1             1 2             4 3             9 4             16 5             25 6             36 7             49 8             64 9             81

Number ends with 1                 1 and 9 4                 2 and 8 9                 3 and 7 6                 4 and 6 5                 5

For Ex: find the square root for 1156

Now, Split the number 1156 as 11 and 56

Check where the first split lies between the nearest squares.

9 ≤ 11 ≤ 16

3² ≤ 11 ≤ 4²

The lowest nearest one has to be taken here. Means, we are going to take 3.
So, the result of the first number will be 3

Multiple with n+1 number, for ex, the lowest nearest one is 3, then n=3.

So, multiple n with n+1 as below

3 * 4 = 12

Check whether 12 is less than 11 or not.

Since the unit number of 1156 is 6, as per the table the number can be 4 or 6.

If it is less take 4 else 6.

Since 12 is greater than 11, we are going to take 6.

So, the square root of 1156 is 36.

One More Ex:

Let check for 2401

Split number 24 and 01

16 ≤ 24 ≤ 25

4² ≤ 24 ≤ 5²

4*5 = 20

Unit digit is 1, so the result of end number can be 1 and 9

24 is the first split one,

Check 20 with 24 is greater than or less than the first split number,

20 < 24

So take 9.

Result = 49

Let check for 1681

Split number 16 and 81

16 ≤ 16 ≤ 25

4²  ≤ 16 ≤ 5²

4*5 = 20

Unit digit is 1, so the result of end number can be 1 and 9

16 is the first split one,

Check whether 16 with 20, 20 > 16, and so take 1.

Result = 41