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Banking Exam Preparation – “Square and Square Root”

Banking Exam Preparation – “Square and Square Root”

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

Table – 1

101492401512601999801
204482304522704989604
309472209532809979409
416462116542916969216
525452025553025959025
636441936563136948836
749431849573249938649
864421764583364928464
981411681593481918281
10100401600603600908100
11121391521613721897921
12144381444623844887744
13169371369633969877569
14196361296644096867396
15225351225654225857225
16256341156664356847056
17289331089674489836889
18324321024684624826724
1936131961694761816561
2040030900704900806400
2144129841715041796241
2248428784725184786084
2352927729735329775929
2457626676745476765776

 

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

Table – 2

X50-X50+X100-XLast Two Digits
149519901
248529804
347539709
446549616
545559525
644569436
743579349
842589264
941599181
1040609000
1139618921
1238628844
1337638769
1436648696
1535658525
1634668456
1733678389
1832688224
1931698161
2030708000
2129717941
2228727884
2327737729
2426747676

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

72 = 49,   82 = 64, 92 = 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’

212  = 441   than x = 21

than       50-x = 29

50+x = 71

100-x = 79

212 = 441,   292 = 841,   712 = 5041,    792 = 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

  1. If    AB – X2 <   X/2  than answer will be x means YZ less than 25,
  2. If   X/2  ≤ AB – X2  ≤ X than answer will be 50 – x means YZ between 25 to 50,
  3. If  X <  AB – X2 3X/2 + 0.5 than answer will be 50 + x means YZ between 50 to 75,
  4. If AB – X2  >   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 – X2  =  67 – 82 = 67 – 64 = 3

Than                      3 < 4

Means AB – X2 <

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:

172                                                                          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 832 = ?

Solve:  100 – 83 = 17

Than minus answer from original number

Means 83 – 17 = 66

These are first two digit of answer

Now 172 = 289

Than 89 is last two digit of answer

We need to forward 2 to next place means

66+2= 68

Then 832 = 6889

Banking Exam Preparation – “Square and Square Root”

Square of numbers between  80 to 100

Take 112

We need to find 1122 = ?

Add last two digit in number

Means 112+ 12 = 124

Now we need to find last two digits  square

Means 122 = 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

1122 = 12544

– “Square and Square Root”

Square of numbers between 50 to 59

Take number as AB

Than square of AB = AB2 = (A2 + B), B2

Example:

542 = ?

52 + 4, 42 = 25+4, 16 = 29, 16

Than answer 542 = 2916

– “Square and Square Root”

Square of numbers between 40 to 49

Take number as AB

Than square of AB = AB2 = (A2 + B – 1),  (10 – B)2

Example:

462 = ?

42 + 6 – 1,  (10 – 6)2  = 16 + 5,  16  = 21,16

Than 462 = 2116

– “Square and Square Root”

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

AB2 = (10,A)2 + 2x10AB + B2

Example:

672 = (10,6)2 + 2x10x6x7 + 72 = 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 752 = 5625

Banking Exam Preparation – “Square and Square Root”

Miscellaneous

Squaring Numbers that end in 1

A2 = (a – 1)2 + 2a – 1                                                                         512 = 502 + 102 – 1 = 2500 + 101 = 2601

Squaring Numbers that end in 4

A2 = (a + 1)2 – (2a + 1)                                                                     642 = 652 – (128 + 1) = 4225 – 129 = 4096

Squaring Numbers that end in 6

A2 = (a – 1)2 + (2a – 1)                                                                       562 = 552 + 112 – 1 = 3025 + 111 = 3136

Squaring Numbers that end in 9

A2 = (a + 1)2 – (2a + 1)                                                                     792 = 802 – (158 + 1) = 6400 – 159 = 6341

Squaring Numbers 52 to 99

A2 = [a – (100 – a)]100 + (100 – a)2                                             942 = (94 – 6)100 + 62 = 8836

Squaring Numbers 101 to 148

A2 = [a + (a – 100)]100 + (a – 100)2                                            1062 = (106 + 6)100 + 62 = 11236

Squaring Numbers near 1000

A2 = [a – (1000 – a)]1000 + (1000 – a)2                                     9942 = (994 – 6)1000 + 62 = 988036

A2 = [a + (a – 1000)]1000 + (a – 1000)2                                     10072 = (1007 + 7)1000 + 72 = 1014049

Banking Exam Preparation – “Square and Square Root”

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