# Tricks to Calculate the Square of A Number Quickly: Check Shortcut to Find Square Here!

By Jyoti Bisht|Updated : April 19th, 2022

Master your calculation tricks: Simplification is the most widely asked topic in almost every banking exam. The questions on simplification check your calculation speed and these Square tricks will comprehend "How to find the square of any number". The speed of solving questions completely depends on your good command of topics like tables, squares, cubes, squares and cube roots, multiplication, etc.  If you know the Square tricks to solve all these topics, the time of solving the question will be reduced and hence, accuracy also gets improved. Let's know the shortcut to find the square of a number.

Master your calculation tricks: Simplification is the most widely asked topic in almost every banking exam. The questions on simplification check your calculation speed and these Square tricks will comprehend "How to find the square of any number". The speed of solving questions completely depends on your good command of topics like tables, squares, cubes, squares and cube roots, multiplication, etc.  If you know the Square tricks to solve all these topics, the time of solving the question will be reduced and hence, accuracy also gets improved. Let's know the shortcut to find the square of a number.

In the article, we are sharing the shortcut methods of solving squares quickly.

Attempt Quant Quiz Here

## Base Method of Calculating Squares

Generally, we can calculate the square of a number by the formula (a2 + b2 + 2ab). This formula applies by splitting a number into a and b. For eg. (49)2 can be calculated using this formula by splitting into 40 and 9. But calculating with this method always is a lengthy process and not recommended to follow in the exam.

The base method of calculating squares is an easy method to square 2 and 3 digits numbers easily. The major thing is to find the Base here. The base is referred to as n x 10x where n is 1, 2, 3, and so on. You have to take the value of base i.e, 10x which is nearer to the number.

Let us see the steps to find the square of a number using the Base Method

Step 1: Find Base i.e, n x10x.

Step 2: Case 1: Square the (Number - Base) if Number > Base

Case 2: Square the (Base - Number) if Base > Number.

Make sure the number of digits in this part = number of zeroes in the base, add zeroes if it is of fewer digits, or carry forward extra digits in case of more than the required digits.

Step 3: Case 1: Add (Number - Base) to Number if Number > Base and then multiply by n.

Case 2: Subtract (Base - Number) from Number if Base > Number and then multiply by n.

Step 4: Merge results of Steps 2 and 3. Keep Step 2 result on the right side.

Suppose you have to find the square of 104.

Step 1: Now, here the base is 100 or 102.

Step 2: Here Number > Base or 104 > 100 so, (104 - 100)= 16

Step 3: 1 x (104 + 4) = 108

Step 4: 10816

In this way, you have to calculate the square using the base method. Let us take more examples to have a clear understanding.

Find the square of 99.

Step 1: Here, the base is 100 or 102.

Step 2: 100 > 99 (100- 99)= 01 (Here we added one zero to the left side of square number to make it a 2 digit number)

Step 3: 1 x (99 - 1) = 98

Step 4: 9801

Find the square of 119.

Step 1: Base is 100 or 102.

Step 2: (119- 100)= 3 61 (Here 3 will be carried forward as we need only 2 digits at this side)

Step 3: 1 x (119 + 19) = 138 + 3 carry = 141

Step 4: 14161

Find the square of 198

Step 1: Now, here the base is 200 or 2 x 102.

Step 2: (200- 198)= 04 (Here we added one zero to the left side of square number to make it a 2 digit number)

Step 3: 2 x (198- 2) = 392

Step 4: 39204

Find the square of 482

Step 1: Now, here the base is 500 or 5 x 102.

Step 2: (500- 482)= 3 24 (Here 3 will be carried forward as we need only 2 digits on this side)

Step 3: 5 x (482- 18) = 2320 + 3 carry = 2323 (Here we had multiplied it by 5 as the base was 5 x 10)

Step 4: 232324

Find the square of 1012

Step 1: Now, here the base is 1000 or 1 x 103.

Step 2: (1012- 1000)= 144 (Here we will keep three digits as the number of zeroes in the base is 3).

Step 3: (1012 + 12) = 1024

Step 4: 1024144

In the exam, you have don't have to write the individual steps. Just start calculating mentally and write the final value. After practicing, you will be able to solve this quickly.

Calculate the following squares using the base method and answer in the comment section.

(A) (93)2      (B) (216)2         (C) (1001)2       (D) (3014)2

The base method is useful when numbers are nearer to the base as it will become more calculating when the difference between numbers and base becomes larger. To overcome such calculation, we are introducing one more method i.e., the Duplex Method.

## Duplex Method to Calculate Squares

To understand this method, at first, you must know how to calculate the duplex of the numbers.

Dup (a) = a2

Dup (ab) = 2 x a x b

Dup (abc) = 2 x a x c + b2

Dup (abcd) = 2 x a x d + 2  x b x c

Now let`s start calculating squares using this method.

(A) Method of calculating the square of a number ab.

It will be Dup a | Dup ab | Dup b

Calculate the square of 42

Dup 4 | Dup 42 | Dup 2

42    |2 x 4 x 2|   22

16   |   1 6       |    4   (Keep only one digit in each part except the first one)

1764

(B) Method of calculating the square of a number abc.

Dup a | Dup ab |    Dup abc  | Dup bc   | Dup c

Find the square of 145

Dup 1 | Dup 14 |    Dup 145      | Dup 45   | Dup 5

12    |2 x 1 x 4| 2 x 1 x 5 + 42 |2 x 4 x 5 |   52

1      |   8       |    2 6              | 4 0         |   2 5

21025

(C) Method of calculating the square of a number abcd.

Dup a | Dup ab |    Dup abc   |   Dup abcd  |    Dup bcd    | Dup cd | Dup d

Find the square of 1234

Dup 1 | Dup 12 |    Dup 123      |         Dup 1234        |    Dup 234    | Dup 34 | Dup 4

12    |2 x 1 x 2| 2 x 1 x 3 + 22 |2 x 1 x 4 + 2 x 2 x 3 |2 x 2 x 4 + 32|2 x 3 x 4| 42

1      |   4       |    1 0              |              2 0            |   2 5             |     2 4   | 1 6

1522756

This is the way to solve squares using the duplex method. But in exams, don`t write steps. Just start calculating the duplex from the right-hand side and write the final answer. Practice solving squares using this method without steps. You can calculate any number of digits from this method. The only need for this method is to know how to calculate the duplex of the numbers.

Calculate the following squares using the duplex method and answer in the comment section.

(A) (87)2      (B) (529)2         (C) (1991)2       (D) (5018)2

Let us see some more tricks of solving squares of the numbers ending with digits 1, 5, 6, and 9.

## Trick to Calculate Squares of Numbers ending with Digit 5

Step 1: We all know 52 is 25. In the squares of numbers ending with 5, just write 25 on the right-hand side of the answer

Step 2: First digit of the number x Successive digit of the first number.

Calculate 252 = 2 x 3 | 25 = 625

Calculate 552 = 5 x 6 | 25 = 3025

Calculate 852 = 8 x 9 | 25 = 7225

Calculate 1252 = 12 x 13 | 25 = 15625

Calculate 3252= 32 x 33 | 25 = 105625

In the same way, you can calculate the square of other numbers ending with digit 5. You just need to strengthen your multiplication skills.

## Trick to Calculate Squares of Numbers ending with Digit 6

Suppose you have to find the square of 76.

Step : (Number - 1)2 + Number + (Number - 1)

(76)2= (75)2 + 75 + 76 = 5625 + 151 = 5776 (Calculate square of number ending with digit 5 using the above method.)

(146)2= (145)2 + 145 + 146 = 21025 + 291= 21316

(1006)2= (1005)2 + 1005 + 1006 = 1010025+ 2011= 1012036

To calculate squares of numbers ending with digit 6, you must know how to calculate squares of numbers ending with digit 5 and fast multiplication skills as it is the foremost requirement.

## Trick to Calculate Squares of Numbers ending with Digit 4

Suppose you have to find the square of 64.

Step : (Number + 1)2 - Number - (Number + 1)

(64)2= (65)2 - 65 - 64 = 4225 - 129 = 4096(Calculate square of number ending with digit 5 using the above method.)

(294)2= (295)2 - 295 - 294 = 87025 - 589= 86436

(3004)2= (3005)2 - 3005 - 3004 = 9030025 - 6009= 9024016

Again, you must know how to calculate squares of numbers ending with digit 5 with strong multiplication skills to calculate squares of numbers ending with digit 4.

## Trick to Calculate Squares of Numbers ending with Digit 1

Suppose you have to calculate the square of 91.

Step : (Number - 1)2 + Number + (Number + 1)

(91)2= (90)2 + 90 + 91 = 8100 + 181 = 8281

(161)2= (160)2 + 160 + 161 = 25600 + 321 = 25921

(921)2= (920)2 + 920 + 921 = 846400 + 1841 = 848241 (Calculate 922 mntally using base method)

(1201)2= (1200)2 + 1200 + 1201 = 1440000 + 2401 = 1442401

In the same way, you can calculate the square of other numbers ending with digit 1. For this, you must remember squares up to 20 and strong addition calculation mentally.

## Trick to Calculate Squares of Numbers ending with Digit 9

Suppose you have to calculate the square of 79.

Step : (Number + 1)2 - Number - (Number + 1)

(79)2= (80)2 - 80 - 79 = 6400 - 159 = 6241

(159)2= (160)2 - 160 - 1659 = 25600 - 319 = 25281

(579)2= (580)2 - 580 - 579 = 336400 - 1159 = 335241 (Calculate 922 mntally using base method)

(1239)2= (1240)2 - 1240 - 12039 = 1537600 - 2479 = 1535121 (Calculate 1242 using duplex method)

For this also, you must possess strong multiplication skills.

## Trick to Calculate Squares of Numbers in the range of 51 to 70

Step : [25 + (Number - 50) | (Number - 50)2]

(51)2= 25 + 1 | 01 = 2601

(57)2= 25 + 7 | 49 = 3249

(66)2= 25 + 16 | 256 = 41 | 2 56 = 43 | 56 = 4356 (Keep only 2 digit on right side)

(69)2= 25 + 19 | 361 = 44 | 3 61 = 47 | 61 = 4761 (Keep only 2 digit on right side)

## Trick to Calculate Squares of Numbers in the Range of 31 to 50

Step : [25 -  (50 - Number) | (50 - Number)2]

(49)2= 25 - 1 | 01 = 2401

(43)2= 25 - 7 | 49 = 1849

(37)2= 25 - 13 | 169 = 12 | 1 69 = 13 | 69 = 1369 (Keep only 2 digit on right side)

(31)2= 25 - 19 | 361 = 6 | 3 61 = 9 | 61 = 961 (Keep only 2 digit on right side)

### Another method: (a + b) (a - b) + b2

(88): it is 100 - 12 or a = 100 and b  = 12

So, (88)= (88 + 12) (88 - 12) + 122 = 76 x 100 + 144 = 7744

(104)= (104 + 4) (104 - 4) + 42 = 108 x 100 + 146 = 10816

(438)(438 + 38) (438- 38) + 382 = 476 x 400 + 1444 = 191844

Calculate the following squares using any of the above mentioned method:

(A) (59)2           (B) (876)2             (C) (1441)2             (D) (995)2               (E) (1441)2                (F) (78)2

So, this was all about short tricks of squares. Practice these methods while calculating squares. In the upcoming articles, we will also cover the short tricks to calculate other topics like multiplication, cubes, square and cube roots, etc. Stay connected and keep going with practice.

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## FAQs

• With the help of the square tricks, candidates can find a square of any number in the Quantitative Section for the bank exam 2022. Divide the number into two parts and determine the square of each of the digits separately. Put these numbers together now. Each number should be written in both the ones and tens position (for example, 32 should be written as 09).

• The aspirants will get a number of short square tricks in this article which will surely save your time and speed up your overall performance in Bank Exams 2022. Take the nearest number with zeroes, such as 112, as an example. The closest number with a zero in this case is 100. So, by adding and subtracting 12 from the basic number, you can get two numbers: 100 and 124.

• You can practice with the shortcut to find the square of a number or 31 to 50 range of numbers for bank exams 2022. The basic method of computing squares is a simple way to square two and three-digit values. The foundation is known as n x 10x, where n is 1, 2, 3, and so on. You must use the base value, i.e. 10x, which is closer to the number.

• For any competitive exam, shortcut strategies for squares, square roots, and multiplication are essential. These shortcut tactics in the Quantitative Aptitude part would be useful for those preparing for competitive bank exams such as IBPS PO, SBI PO, IBPS Clerk, RBI Assistant, RBI Grade B and others.

• To begin, we must memorize the unit digits for all squares from 1 to 10. The unit digit of squares is shown in the diagram below. Let's take the example of 4624.

• The final two digits are grouped first, followed by the remaining digits.
• Check the square root's unit digit position, which is 4, to see if it ends in 2 or 8.
• Take a look at the first two digits – 46. It is located between 6 and 72 (364649).
• As a result, the square root's tenth digit will be 6.
• We must now determine if the number is 62 or 68. Multiply 6 by the following term in the series, i.e. 7. 6*7=4246
• Because 46 is greater than 42, the square root of 4624 will be greater than 68. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com