Square Root Tricks in Maths for Fast Calculation

By PARUL RISHI|Updated : July 20th, 2022

Square of numbers plays an important role in the quantitative aptitude and Reasoning section of SSC and Railway Exams. At least 1 to 2 questions are asked directly and 2 to 3 questions are asked in between the questions.
So, to help you score better in the exam in this post we are sharing some important tricks on how to calculate square within seconds provided you practice the square number questions through this type of tricks. The tricks are divided in 5 different cases which are as follows:

Case 1: Number with the last digit of 5

Case 2: Number between 30 and 50

Case 3: Number between 50 and 80

Case 4: Number between 80 and 100

Case 5: Number between 100 and 130

Let’s take a look at the square of numbers from 1 to 30:

Number

Square

Number

Square

1

1

16

256

2

4

17

289

3

9

18

324

4

16

19

361

5

25

20

400

6

36

21

441

7

49

22

484

8

64

23

529

9

81

24

576

10

100

25

625

11

121

26

676

12

144

27

729

13

169

28

784

14

196

29

841

15

225

30

900

1st Case: Square with the last digit of 5

  1. 352 = 1225

Last two digit is the square of 5 that is 25 – (i)

For first two-digit

ADD -> 3+1 = 4

MULTIPLY-> 3*4 = 12 – (ii)

Combine both (i) & (ii), we get square of 35

352 = 1225

  1. 652 = 4225

Last two digit is square of 5 = 25 – (i)

For first two-digit

ADD -> 6+1 = 7

MULTIPLY -> 6*7 = 42 – (ii)

Combine both (i) & (ii), we get a square of 65

652 = 4225

  1. 1252 = 15625

The last two digit are square of 5 = 25 – (i)

For the first three-digit:

ADD -> 12 + 1 = 13

MULTIPLY -> 12 * 13 = 156 - (ii)

Combine both (i) & (ii), we get square of 125

1252 = 15625

2nd Case: Square between 30 to 50

Square between 30 to 50

*Square of digit between 32 to 99 are always in four digits.

  1. 372 = 1369

Step 1: 50 – 37 = 13

Square of 13 = 169 – Take the last two digit – (i)

Step 2: 25 – 13 = 12 – (ii)

Combine both in this manner

   12 – (ii)

   + 169 – (i)

= 1369

The square of 37 is 1369

  1. 462 = 2116

Step 1: 50 - 46 = 4

Square of 4 = 16 – Take the last two digit – (i)

Step 2: 25 – 4 = 21 – (ii)

Combine both in this manner

21 – (ii)

 +16 – (i)

2116

The square of 46 is 2116

3rd Case: Square between 50 to 80

  1. 622 = 3844

Step 1: 62 – 50 = 12

Square of 12 = 144 – Last two digit – (i)

Step 2: 25 + 12 = 37 – (ii)

Combine both in this manner

37 – (ii)

+144 – (i)

3844

The square of 62 is 3844

  1. 782 = 6084

Step 1: 78 – 50 = 28

Square of 28 = 784 – Last two digit – (i)

Step 2: 25 + 28 = 53 – (ii)

53

+784

6084

The square of 78 is 6084

4th Case: Square between 80 to 100

  1. 882 = 7744

Step 1: 100 - 88 = 12

Square of 12 = 144 – Last two digit – (i)

Step 2: 88 – 12 = 76

Combine both in this manner

76 – (ii)

+144 – (i)

7744

Square of 88 is 7744

  1. 942 = 8836

Step 1: 100 – 94 = 6

Square of 6 = 36 – Last two digit – (i)

Step 2: 94 - 6 = 88 – (ii)

Combine both in this manner

88

+ 36

8836

The square of 94 is 8836

5th Case: Square between 100 to 130

*Square of digit between 100 to 316 are always in five digits

  1. 1062 = 11236

Step 1: 106 - 100 = 6

Square of 6 = 36 – Last two digit – (i)

Step 2: 106 + 6 = 112 – (ii)

Combine both in this manner

112 – (ii)

+    36 – (i)

11236

We have square of 106 = 11236

  1. 1262 = 15876

Step 1: 126 - 100 = 26

Square of 26 = 676 – Last two digit – (i)

Step 2: 126 + 26 = 152 – (ii)

Combine both in this manner

152

+  676

15876

The square of 126 is 15876 

Stay tuned!

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