How To Find Square Roots of Numbers Quickly

How To Find Square Roots of Numbers Quickly

In our previous post we saw how to find the cube root of a perfect cube in seconds. Today we will discuss a vedic maths trick to find out square root of perfect squares quickly. This method uses the same approach which we have seen in the cube root method.  To proceed its very necessary for us to memorize the square of first ten natural numbers.

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

From the above table you can observe that we have 1 in the number column and 1 in the square column. In the same way, in the 9th row we have 9 in the number column and 1 in the square column. From this we can conclude that if the number ends in 1, the square root ends in 1 or 9 . Similarly if the number ends in 4 the square root ends in 2 or 8. If the number ends in 9, the square root ends in 3 or 7. If the number ends in 6, the square root ends in 4 or 6. If the number ends in 5, the square root ends in 5. If the number ends in 0, the square root also  ends in 0. The below table summarize this thing. You should memorize this table.

Last digit of square	Last digit of square root
1	1 or 9
4	2 or 8
9	3 or 7
6	4 or 6
5	5
0	0

From the above tables you can find that a perfect square never ends  with 2,3,7, or 8

Below is the another table of square of numbers from 10 to 100.  This table will help us to find the square roots quickly.

Number	Square
10	100
20	400
30	900
40	1600
50	2500
60	3600
70	4900
80	6400
90	8100
100	10000

Lets now try to find the square root of 9801

Step 1: The last digit of the number 9801 is 1 therefore the last digit of the square root will be either 1 0r 9. The answer for now will be _1 or _9

Step: 2 The number 9801 lies between 8100 (square of 90) and 10000 ( square of 100). Therefore the answer lies between 90 and 100.  From the first step we know that the  square  ends in either 1 or 9. So the answer can be 91 or 99

Step 3: Now we pick the number which is closer to the square. Since 9801 is closer to the bigger number 10,000 we will take the number number 99 as the answer.   So our answer becomes 99

Lets find the square root of 5184 through the same shortcut method

Step 1: Number ends in 4. So square root ends in either 2 or 8. Answer at this stage can be _2 or _8

Step 2: 5184 lies between 4900 and 6400, the square of 70 and 80.  From the first step the answer at this stage becomes 72 or 78

Step 3: 5184 is closer to the smaller number 4900. Thus we take smaller number 72 as our correct answer.

I hope you have understood the method, if you have any problem let us know in comments and we will do our best to help you.