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. This method is applicable only for perfect squares. Square root questions asked in bank exams are usually perfect squares. Refer How to check if a number is a perfect square? to find out if a given number is a perfect square.
Steps to find the square root of any number
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 the 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

Let’s 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 the 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 the first pair 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
Shortcut to find the square root of any 3 digit number
Example 1: √784=?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
7 84
Step 2: To get the ten’s place digit,
We find that nearest square to the 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 x 3=6
ten’s place digit of original number > Multiplication result
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
Shortcut to find the square root of any 4 digit number
Example 2: √3721?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
37 21
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (37)is 36 and√36=6
Therefore ten’s place digit=6
Step 3: To get the unit’s place digit,
We notice that the number ends with 1, So the unit’s place digit of the square root should be either 1 or 9(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(6) and its consecutive number(7) we get,
6 x 7=42
ten’s place digit of an original number<Multiplication result
37 < 42
So we need to select the lesser number (1) as the unit’s place digit of the square root.
Unit’s place digit =1
Ans:√3721=61
Example 3: √6889?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
68 89
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (68)is 64 and√64=8
Therefore ten’s place digit=8
Step 3: To get the unit’s place digit,
We notice that the number ends with 9, So the unit’s place digit of the square root should be either 3 or 7(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(8) and its consecutive number(9) we get,
8 x 9 =72
ten’s place digit of an original number<Multiplication result
68 < 72
So we need to select the lesser number (3) as the unit’s place digit of the square root.
Unit’s place digit =3
Ans:√6889=83
Shortcut to find the square root of any 5 digit number
Example 4: √64516
Step 1: We start by grouping the numbers in pairs of two from the right as follows
645 16
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (645)is 625 and√625=25
Therefore ten’s place digit=25
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(25)and its consecutive number(26)we get,
25 x 26=650
ten’s place digit of an original number<Multiplication result
645< 650
So we need to select the lesser number (4) as the unit’s place digit of the square root.
Unit’s place digit =4
Ans:√64516=254
Shortcut to find the square root of any 6 digit number
Example 5: √126736
Step 1: We start by grouping the numbers in pairs of two from the right as follows. For a 6 digit number, this is how it should be paired.
1267 36
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (1267)is 1225 and√1225=35
Therefore ten’s place digit=35
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(35)and its consecutive number(36)we get,
35 x 36=1260
ten’s place digit of original number>Multiplication result
1267>1260
So we need to select the greater number (6) as the unit’s place digit of the square root.
Unit’s place digit =6
Ans:√126736=356
Example 6: √207025
Step 1: We start by grouping the numbers in pairs of two from right as follows. For a 6 digit number, this is how it should be paired.
2070 25
Step 2: To get the tenth place digit,
We find that nearest square to the first group (2070) is 2025 and√2025=45. Therefore ten’s place digit=45
Step 3: To get the unit’s place digit,
We notice that the number ends with 5, So the unit’s place digit of the square root should be 5(Refer table).
Skip all the other steps for a number ending in 5
Unit’s place digit =5
Ans:√207025=455
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