Kerala PSC - Trick to mentally calculate square roots in Seconds

In this post you will Learn how to mentally calculate cube roots. By learning this simple system you will be able to instantly calculate the cube root of the a number and please keep in mind that this method will not work with cubes of numbers greater than 99. Also this method only works when the cube root is a natural number (integer).

Step 1: Learn the Squares of 0 to 9

To master the system you must learn by heart the squares of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each square.

Number	Square	Last Digit
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

Note how the last digits for the squares of 1 and 9 are both 1.
Note how the last digits for the squares of 2 and 8 are both 4.
Note how the last digits for the squares of 3 and 7 are both 9.
Note how the last digits for the squares of 4 and 6 are both 6.

Step 2: Determine the Square Root

Ignore the last two digits of the number called out by the spectator and choose the memorised square which is just lower (or equal) to the remaining number. The corresponding square root is the first digit. of your answer

Now consider the last digit of the number called out by the spectator. If this is 0 or 5, then you immediately know that the last digit of your answer is also 0 or 5.

In all other cases, the last digit of the number called out will indicate two possible values for the last digit of the square root. For example, if the last digit is 9, then the square root may end in either 3 or 7.

To determine whether the lower or higher value should be taken, multiply the first digit of your answer by one greater than itself. If this is greater than the first part of the number called by the spectator (i.e., ignoring the last two digits), then the last digit of your answer is the lower of the two possible values. Otherwise the last digit is the higher value.

For example if the number called is 2809, the square root could be either 53 or 57. Since 5 x 6 = 30, and 28 is less than 30, the answer is 53.

Examples

Spectator Calls	Ignore Last 2	Lower Square	First Digit (a)	Last Digit	a(a+1)	Square Root
144	1	1	1	2 or 8	2	12
784	7	4	2	2 or 8	6	28
1369	13	9	3	3 or 7	12	37
2401	24	16	4	1 or 9	20	49
2809	28	25	5	3 or 7	30	53
3600	36	36	6	0		60
5041	50	49	7	1 or 9	56	71
7396	73	64	8	4 or 6	72	86
8836	88	81	9	4 or 6	90	94

Step 3: Practice, Practice, Practice ! 

Before going for exams, you should practice until you can calculate the cube root instantly and without error. If you can't do this, then practice some more! To practice and assess your ability, you can use the test below.