Shortcut to find squareroot of any number
In every bank exam you are asked either to find the square root or cube root of a number. By knowing the shortcut to find the square root of a number, you will be able to find out the square root of any number within seconds.
Now lets go through the steps…
Step 1: First of all group the number in pairs of 2 starting from the right.
Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.
Step 3: To get the unit’s place digit of the square root
Remember the following
If number ends in

Unit’s place digit of the square root

1

1 or 9(101)

4

2 or 8(102)

9

3 or 7(103)

6

4or 6(104)

5

5

0

0

Lets see the logic behind this for a better understanding
We know,
1^{2}=1
2^{2}=4
3^{2}=9
4^{2}=16
5^{2}=25
6^{2}=36
7^{2}=49
8^{2}=64
9^{2}=81
10^{2}=100
Now, observe the unit’s place digit of all the squares.
Do you find anything common?
We notice that,
Unit’s place digit of both 1^{2} and 9^{2 }is 1.
Unit’s place digit of both 2^{2} and 8^{2} is 4
Unit’s place digit of both 3^{2} and 7^{2} is 9
Unit’s place digit of both 4^{2} and 6^{2} is 6.
Step 4: Multiply the ten’s place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from left.
Remember,
If first pair of the original number > Result obtained on multiplication then select the greater number out of the two numbers as the unit’s place digit of the square root.
If firstpair of the original number < the result obtained on multiplication,then select the lesser number out of the two numbers as the unit’s place digit of the square root.
Let us consider an example to get a better understanding of the method
Example 1: √784=?
Step 1: We start by grouping the numbers in pairs of two from right as follows
7 84
Step 2: To get the ten’s place digit,
We find that nearest square to first group (7) is 4 and √4=2
Therefore ten’s place digit=2
Step 3: To get the unit’s place digit,
We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get,
2×3=6
ten’s place digit of original number > Multiplication result
7>6
7>6
So we need to select the greater number (8) as the unit’s place digit of the square root.
Unit’s place digit =8
Ans:√784=28