**Banking Exam Preparation – “Square and Square Root”**

**Unit digit of any square number – “0, 1, 4, 5, 6, 9”**

**Table – 1**

1 | 01 | 49 | 2401 | 51 | 2601 | 99 | 9801 |

2 | 04 | 48 | 2304 | 52 | 2704 | 98 | 9604 |

3 | 09 | 47 | 2209 | 53 | 2809 | 97 | 9409 |

4 | 16 | 46 | 2116 | 54 | 2916 | 96 | 9216 |

5 | 25 | 45 | 2025 | 55 | 3025 | 95 | 9025 |

6 | 36 | 44 | 1936 | 56 | 3136 | 94 | 8836 |

7 | 49 | 43 | 1849 | 57 | 3249 | 93 | 8649 |

8 | 64 | 42 | 1764 | 58 | 3364 | 92 | 8464 |

9 | 81 | 41 | 1681 | 59 | 3481 | 91 | 8281 |

10 | 100 | 40 | 1600 | 60 | 3600 | 90 | 8100 |

11 | 121 | 39 | 1521 | 61 | 3721 | 89 | 7921 |

12 | 144 | 38 | 1444 | 62 | 3844 | 88 | 7744 |

13 | 169 | 37 | 1369 | 63 | 3969 | 87 | 7569 |

14 | 196 | 36 | 1296 | 64 | 4096 | 86 | 7396 |

15 | 225 | 35 | 1225 | 65 | 4225 | 85 | 7225 |

16 | 256 | 34 | 1156 | 66 | 4356 | 84 | 7056 |

17 | 289 | 33 | 1089 | 67 | 4489 | 83 | 6889 |

18 | 324 | 32 | 1024 | 68 | 4624 | 82 | 6724 |

19 | 361 | 31 | 961 | 69 | 4761 | 81 | 6561 |

20 | 400 | 30 | 900 | 70 | 4900 | 80 | 6400 |

21 | 441 | 29 | 841 | 71 | 5041 | 79 | 6241 |

22 | 484 | 28 | 784 | 72 | 5184 | 78 | 6084 |

23 | 529 | 27 | 729 | 73 | 5329 | 77 | 5929 |

24 | 576 | 26 | 676 | 74 | 5476 | 76 | 5776 |

**Read “Table 2” and check last two digits from “Table 1”**

**Table – 2**

X | 50-X | 50+X | 100-X | Last Two Digits |

1 | 49 | 51 | 99 | 01 |

2 | 48 | 52 | 98 | 04 |

3 | 47 | 53 | 97 | 09 |

4 | 46 | 54 | 96 | 16 |

5 | 45 | 55 | 95 | 25 |

6 | 44 | 56 | 94 | 36 |

7 | 43 | 57 | 93 | 49 |

8 | 42 | 58 | 92 | 64 |

9 | 41 | 59 | 91 | 81 |

10 | 40 | 60 | 90 | 00 |

11 | 39 | 61 | 89 | 21 |

12 | 38 | 62 | 88 | 44 |

13 | 37 | 63 | 87 | 69 |

14 | 36 | 64 | 86 | 96 |

15 | 35 | 65 | 85 | 25 |

16 | 34 | 66 | 84 | 56 |

17 | 33 | 67 | 83 | 89 |

18 | 32 | 68 | 82 | 24 |

19 | 31 | 69 | 81 | 61 |

20 | 30 | 70 | 80 | 00 |

21 | 29 | 71 | 79 | 41 |

22 | 28 | 72 | 78 | 84 |

23 | 27 | 73 | 77 | 29 |

24 | 26 | 74 | 76 | 76 |

Example:

674041 is one number.

How can we find square root of this number?

We take answer as XYZ

Let’s take 674041 as ABCDEF

**STEP-1**

Take ABCDEF in the group of 2 digits

AB = 67, CD = 40, EF = 41

From AB we find first digit of our Answer means X

7^{2 }= 49, 8^{2 }= 64, 9^{2} = 81

67 is between 64 and 81

**Then X = 8**

**STEP-2**

We find 4 different numbers from EF

EF = 41

We know from Table 1 that square of these 4 numbers have last two digits ‘41’

21^{2 } = 441 than x = 21

than 50-x = 29

50+x = 71

100-x = 79

21^{2} = 441, 29^{2} = 841, 71^{2} = 5041, 79^{2} = 6241

Than last two digits of Answer YZ may 21, 29, 71, 79

Than Answer XYZ may be

**XYZ = 821 or 829 or 871 or 879**

** ****STEP-3**

We need to recheck first two digits of question AB

- If
**AB – X**^{2}<**X/2**than answer will be x means YZ less than 25, - If
**X/2 ≤ AB – X**than answer will be 50 – x means YZ between 25 to 50,^{2}≤ X - If
**X < AB – X**^{2}<**3X/2 + 0.5**than answer will be 50 + x means YZ between 50 to 75, - If
**AB – X**^{2 }>**3X/2**+**0.5**than answer will be 100 – x means YZ greater than

We know AB = 67

And X = 8

And = 4

Than AB – X^{2} = 67 – 8^{2} = 67 – 64 = 3

Than 3 < 4

Means AB – X^{2}** < **

Then YZ will be less than 25 means x

Then YZ = 21

Then answer **XYZ = 821**

** – “Square and Square Root”**

Unit number of any digit Unit digit of Square number

1 or 9 1

2 or 8 4

3 or 7 9

4 or 6 6

5 5

0 0

Example:

17^{2} 289

Unit digit of number 17 is 7 Unit digit of square is 9

**Banking Exam Preparation – “Square and Square Root”**

** **Square of numbesr between 80 to 100

Take 83

We need to find 83^{2} = ?

Solve: 100 – 83 = 17

Than minus answer from original number

Means 83 – 17 = 66

These are first two digit of answer

Now 17^{2} = 289

Than 89 is last two digit of answer

We need to forward 2 to next place means

66+2= 68

Then **83 ^{2} = 6889**

**Banking Exam Preparation – “Square and Square Root”**

Square of numbers between 80 to 100

Take 112

We need to find 112^{2} = ?

Add last two digit in number

Means 112+ 12 = 124

Now we need to find last two digits square

Means 12^{2} = 144

Than last two digit of answer is 44 and we need to forward 1 to next place

Means 124+1 = 125

Then answer 12544

**112 ^{2} = 12544**

** – “Square and Square Root”**

Square of numbers between 50 to 59

Take number as AB

Than square of AB = AB^{2} = (A^{2} + B), B^{2}

Example:

54^{2} = ?

5^{2} + 4, 4^{2} = 25+4, 16 = 29, 16

Than answer **54 ^{2} =**

**2916**

** – “Square and Square Root”**

Square of numbers between 40 to 49

Take number as AB

Than square of AB = AB^{2} = (A^{2} + B – 1), (10 – B)^{2}

Example:

46^{2} = ?

4^{2} + 6 – 1, (10 – 6)^{2} = 16 + 5, 16 = 21,16

Than **46 ^{2} = 2116**

** – “Square and Square Root”**

Square any Two Digit Number (a = 10’s digit & b = 1’s digit)

AB^{2} = (10,A)^{2} + 2x10AB + B^{2}

Example:

67^{2} = (10,6)^{2} + 2x10x6x7 + 7^{2} = 100×36 + 840 + 49 = 3600 + 840 + 49 = 4489

**Banking Exam Preparation – “Square and Square Root”**

Square of number with unit digit 5

Let’s take number as AB where B = 5

Multiply A with A + 1

Last two digit of answer 25

Example: 75

Than 7×8 = 56

Than **75 ^{2} = 5625**

**Banking Exam Preparation – “Square and Square Root”**

Miscellaneous

Squaring Numbers that end in 1

A^{2} = (a – 1)^{2} + 2a – 1 51^{2} = 50^{2} + 102 – 1 = 2500 + 101 = 2601

Squaring Numbers that end in 4

A^{2} = (a + 1)^{2} – (2a + 1) 64^{2} = 65^{2} – (128 + 1) = 4225 – 129 = 4096

Squaring Numbers that end in 6

A^{2} = (a – 1)^{2} + (2a – 1) 56^{2} = 55^{2} + 112 – 1 = 3025 + 111 = 3136

Squaring Numbers that end in 9

A^{2} = (a + 1)^{2} – (2a + 1) 79^{2} = 80^{2} – (158 + 1) = 6400 – 159 = 6341

Squaring Numbers 52 to 99

A^{2} = [a – (100 – a)]100 + (100 – a)^{2} 94^{2} = (94 – 6)100 + 6^{2} = 8836

Squaring Numbers 101 to 148

A^{2} = [a + (a – 100)]100 + (a – 100)^{2} 106^{2} = (106 + 6)100 + 6^{2} = 11236

Squaring Numbers near 1000

A^{2} = [a – (1000 – a)]1000 + (1000 – a)^{2} 994^{2} = (994 – 6)1000 + 6^{2} = 988036

A^{2} = [a + (a – 1000)]1000 + (a – 1000)^{2} 1007^{2} = (1007 + 7)1000 + 7^{2} = 1014049

**Banking Exam Preparation – “Square and Square Root”**

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