How to Find Square Root in 4 Easy Steps with Shortcut

Competitive exams have at least one question where you have to find the square root of a number in seconds. With the help of this shortcut method, you can find square root of a number within seconds. This method is applicable only for perfect squares. The Square root questions asked in competitive exams/bank exams & entrance 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.

How to Find Square Root Easily Using Shortcut

Below are the steps to find square root of a number easily in seconds.

Step 1: First, 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 the left and put the square root of the square.

Step 3: To get the unit’s place digit of the square root value.

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 used in this method of How to find square root using short cut 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 9² is 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 the 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 this method on how to find square root of any number quickly.

How to find 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,

The 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 to the 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

How to find 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 the 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 to the 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 Easily using shortcut Method

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,

The nearest square to the first group (68)is 64 and√64=8. Therefore ten’s place digit=8

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

How to Find square root of 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 the 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 to the 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

How to find 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 the 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 to the 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 the 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,

The 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 to the table).

Skip all the other steps that are to be used in how to find square root for a number ending in 5

Unit’s place digit =5

Ans:√207025=455

Square root 1 to 25/ Square Root 1 to 30

Number	Square Root of Given Number
1	1
2	1.41
3	1.73
4	2
5	2.23
6	2.44
7	2.64
8	2.82
9	3
10	3.16
11	3.31
12	3.46
13	3.6
14	3.74
15	3.87
16	4
17	4.12
18	4.24
19	4.35
20	4.47
21	4.58
22	4.69
23	4.79
24	4.89
25	5
26	5.09
27	5.20
28	5.29
29	5.39
30	5.48

You may also refer to the square root table 1 to 50.

How to Find Square root using Square Root Formula

n√z = z ^1/n

So here, if we substitute number 2 for n. Then it would be the square root of z.

To Generalise, the above formula can be used to find the nth root of any given number z.

How to Find Square root of a Decimal Number?

You may use the same shortcut “How to find square root on whole numbers” to find square root of a decimal number.

Below are the steps:

Step 1: First, 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 the left and put the square root of the square.

Step 3: To get the unit’s place digit of the square root value.

Step 4: Place the decimal point after the ten’s place digit.

We shall apply the same shortcut to the previous examples with a decimal point added to understand how it works

Example 1: √7.84=?

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,

The 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 to the 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

Step 5: Now, place the decimal point after the ten’s place digit (2)

Ans:√7.84=2.8

Example 2: √37.21?

Step 1: Grouping in pairs

37 21

Step 2: Find the ten’s place digit which is 6.

Step 3: Find the unit’s place digit which is 1.

Step 4: Now, place the decimal point next to the ten’s place digit to arrive at your answer.

Ans:√37.21=6.1

Faqs

In a nutshell, you can use how to find square root shortcut on the whole number and a decimal number. With these simple tricks and tips, you are sure to rock your exams.