## Perfect Square Series

Perfect square series is an arrangement of numbers in a certain order where each numbers are square of a number. So, in that series of numbers some numbers are missing. You need to observe and find the missing number of that series of numbers.

This type of problem are given in Quantitative Aptitude part which is a very essential in competitive exam. And, it is very simple to work with perfect square root numbers. You can easily obtain the result of perfect square number. So, how you get Perfect square missing numbers by memorize square and square root numbers shortcut tricks.

### Few Important things about Perfect Square Series

The square of same number and the square result of a number which is equal to the square of another same element. In mathematical world, a square number or perfect square is number of an integer positive integer that is the square of an same integer number always and the numbers are non-negative.

So, in other words, we say it is the result of product of multiplication of some positive integer numbers with itself always. For example, we consider 4 is a result of square numbers, since it as 2 × 2 in normal way.

The normal representation of square numbers is n^{2}and that is similar with products of n × n, but it is similar with exponentiation of n^{2},

In Square numbers are positive number. So, we can explain it that a positive number is a square number, where it’s square roots are always integers positive numbers. So, for example, √4 = ±2, so 4 is a square number.

### Perfect Square Series

Now, here we see the some examples that how the Perfect Square Series are arranged how the missing square series are arranged.

### Perfect Square Series: Example #1

841, ? , 2401, 3481, 4761

- 1071
- 1331
- 1411
- 1521

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

29

^{2}= 841

**39**

^{2}= 152149

^{2}= 2401

59

^{2}= 3481

69

^{2}= 4761

**Rough Workspace**

### Perfect Square Series: Example #2

1, 9, 25, ? , 81, 121

- 49
- 56
- 65
- 76

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

1

^{2}= 1

3

^{2}= 9

5

^{2}= 25

**7**

^{2}= 499

^{2}= 81

11

^{2}= 121

**Rough Workspace**

### Perfect Square Series: Example #3

289, 225, 169, ? , 81

- 131
- 119
- 121
- 111

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

17

^{2}= 289

15

^{2}= 225

13

^{2}= 169

**11**

^{2}= 1219

^{2}= 81

**Rough Workspace**

### Perfect Square Series: Example #4

441, 484, 529, 576, ?

- 565
- 605
- 655
- 625

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

21

^{2}= 441

22

^{2}= 484

23

^{2}= 529

24

^{2}= 576

**25**

^{2}= 625**Rough Workspace**

### Perfect Square Series: Example #5

121, 144, 169, ? , 225

- 196
- 199
- 206
- 211

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

11

^{2}= 121

12

^{2}= 144

13

^{2}= 169

**14**

^{2}= 19615

^{2}= 225

**Rough Workspace**

### Perfect Square Series: Example #6

? , 2116, 2209, 2304, 2401, 2500

- 2099
- 2055
- 2025
- 1955

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

**45**

^{2}= 202546

^{2}= 2116

47

^{2}= 2209

48

^{2}= 2304

49

^{2}= 2401

50

^{2}= 2500

**Rough Workspace**

### Perfect Square Series: Example #7

961, 1024, ? , 1156, 1225

- 1109
- 1049
- 1089
- 1005

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

31

^{2}= 961

32

^{2}= 1024

**33**

^{2}= 108934

^{2}= 1156

35

^{2}= 1225

**Rough Workspace**

### Perfect Square Series: Example #8

36, ? , 64, 81, 100, 121

- 45
- 49
- 53
- 57

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

6

^{2}= 36

**7**

^{2}= 498

^{2}= 64

9

^{2}= 81

10

^{2}= 100

11

^{2}= 121

**Rough Workspace**

### Perfect Square Series: Example #9

121, 169, ? , 289, 361

- 205
- 225
- 235
- 255

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

11

^{2}= 121

13

^{2}= 169

**15**

^{2}= 22517

^{2}= 289

19

^{2}= 361

**Rough Workspace**

### Example #10

121, 484, 1089, 1936, ? , 4356

- 2699
- 3025
- 2905
- 3255

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

11

^{2}= 121

22

^{2}= 484

33

^{2}= 1089

44

^{2}= 1936

**55**

^{2}= 302566

^{2}= 4356

**Rough Workspace**

### Example #11

961, 1024, 1089, ? , 1225

- 1156
- 1106
- 1176
- 1206

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

31

^{2}= 961

32

^{2}= 1024

33

^{2}= 1089

**34**

^{2}= 115635

^{2}= 1225

**Rough Workspace**

### Example #12

1849, ? , 2025, 2116, 2209

- 2000
- 1987
- 1899
- 1936

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

43

^{2}= 1849

**44**

^{2}= 193645

^{2}= 2025

46

^{2}= 2116

47

^{2}= 2209

**Rough Workspace**

### Example #13

2500, 2401, 2304, ? , 2116, 2025

- 2284
- 2249
- 2209
- 2193

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

50

^{2}= 2500

49

^{2}= 2401

48

^{2}= 2304

**47**

^{2}= 220946

^{2}= 2116

45

^{2}= 2015

**Rough Workspace**

### Other Types of Number Series

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its a perfect square series, So you have understand the pattern, in first example maintain a same pattern like 21( square) = we know 21 x 21 = 441

Similarly 22(square), 23(square), 24(square), than lastly 25(square) 25 x 25 = 625 ans.

if questions are like this means then it is k if suppose the question is like 0 2 6 12 20 30 then it is not a series of perfect sruares or cubes so if they r perfect squares or cubes then it is k if the que is like this how to solve them and tell me tricks to solve this type of questions

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Just at a single glance it can be said that it is not of perfect square series r cubes.

check the difference between predecessor and successor number, it is a raising even number series.

Whichever May be the number series, the shortcut would be applied only after analyzing the difference.

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