square root shortcut Archives

Shortcut to find Square Root of any Number

In every competitive exam, there is at least one instance where you will have to find the square root of a number quickly. With the help of this shortcut on how 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 competitive exams/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 a 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(10-1)
4	2 or 8(10-2)
9	3 or 7(10-3)
6	4or 6(10-4)
5	5
0	0

Let’s see the logic behind this method to find square root for a better understanding

We know,

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=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 1²and 9²is 1.

Unit’s place digit of both 2² and 8² is 4

And Unit’s place digit of both 3² and 7² is 9

Unit’s place digit of both 4² and 6² 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 a 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

How to find square root shortcut

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

Also, read Square root shortcut Non-perfect squares