**Perfect Square ****Series**

**Perfect Square**

**Series**

**Perfect Square ****Series****:- **A series of numbers that are the perfect squares of another number is called a Perfect Square Series. The Perfect square series is derived from this number sequence, which serves as the series’ parent sequence.

###### The rule we use to put a sequence together sometimes comes from the parent series, and other times it comes from the square series itself. Let’s get started on our comprehension of the Perfect Square Series and the most frequently asked questions on the IBPS PO, SO, SBI Cleric, and other exams like them.

**Perfect Square For Maths **

First, let’s talk about what a **perfect square** is. If we take the square of an integer number, a number is a perfect square. To put it another way, when we square an integer, the end result will always be a perfect square. All whole numbers and their negatives are referred to as integers. The logic dictates that the perfect square series will be a series in which each term is a perfect square. A perfect square series has all positive terms, unlike the perfect cube series. We will need to commit to memory at least the squares of the first thirty numbers in order to solve all square series questions accurately and to save time. They will be listed here, and the majority of them will be used in the subsequent examples.

###### You will be able to guess the squares of a few additional numbers and save time by memorizing this. From the table above, we can see, for instance, that if a number ends in 5, it is either the square of 5, 15, 25, 35,…, or the square of 2, 12, 22, 32,…or 8, 18, 28, 38, etc. In a similar vein, you can see that a number that ends with 0 is the square of 10, 20, 30, etc. The square of 4, 6, 14, 16, 24, 26, and so on is a number that ends in 6.

**First Thirty Squares**

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

121 | 144 | 169 | 196 | 225 | 256 | 289 | 324 | 361 | 400 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

441 | 484 | 529 | 576 | 625 | 676 | 729 | 784 | 841 | 900 |

###### Using this table will save you a lot of time and turn answering square series questions into a fun activity instead of a tedious chore. You will notice that a lot of the questions on the exams will use numbers from this table. We can use this table to deduce the squares even if the numbers are not from this table. For instance, 810000 x 9002 x 30 =Therefore, in addition to assisting you with squares, this table will also assist you in simplifying numerous large numbers that you may come across. Think of it as the language of numbers in math. Let’s solve a few problems.

**Important Solved Examples: **There will be a few different kinds of questions here, just like there are for other number series. A series may be a simple square series that asks you to choose the wrong term or has a missing number. From a set of number series, it could be the wrong series. Let’s look at some examples to see.

**One example: There are a few number series in the options below. Choose the incorrect one from among them:**

**A) 3, 9, 15, 21**

**B) 9, 81, 225, and 441**

**C) 441, 529, 676, and 841**

**D) 900, 841, and 784, 729**

**Ans: ****C) 441, 529, 676, 841**

**Answer Debate:-** ** ****C) 441, 529, 676, 841. **Try to solve this problem without looking at the table above. It takes quite a while. The first series is nothing more than an A.P. with a 6 common difference. We can now see that the second sequence is the perfect square sequence by using the table. The third sequence is a two-tier square series, but instead of 841, we need 900. This series can be made from the series in option A. This is an off-base series. The final series is square as well. So the right choice or some unacceptable series of the four choices introduced above is.

**2nd Example: A term is missing from the following sequence. The options that are listed below contain the missing term. Choose the missing term from the selections below:8, 12, 21, 37, __**

**A) 52 **

**B) 62 **

**C) 72 **

**D) 80**

**Ans: B) ****62**

**Answer Debate:- ****Therefore, the correct choice is B, and the missing term is 37 plus 25 = 62. **The first term is not a square, number 8.The other terms are not perfect cubes, whereas 8 is. As a result, we can say that this series is not a perfect square or cube series. This suggests that it might be a tier-two series. First, we examine the difference between the two starting terms, which is equal to 4 or 22 and is 8 and 12.

###### The difference between 21 and 12 is then equal to 9 and 32. Therefore, there is a pattern. This rule will be referred to as the rule of the series if we are able to observe the same pattern in the subsequent term. 42 is the difference between 37 and 21. Accordingly this is the standard that you have been searching for. These are square two-tier series. Thus, the final term can be obtained by adding 52, or 37, to the final term.

**Best Questions for Practice: **

**Q 1:One of the following sequences contains an incorrect entry. Choose that series from the available choices below:**

**A) 2, 4, 16, 256 **

**B) 1, 1, 1, 1 **

**C) 3, 12, 156, 244922 **

**D) 2, 2, 2, 2**

**Ans: C) 3, 12, 156, 244922**

**Q 2:Which of the following sequences is not a derivative of a perfect square series or a perfect square series itself?**

**A) 1, 1, 1**

**B) 2, 2, 2, 2**

**C) 3, 6, 30, 870**

**D) 3, 3, 3, 3 **

**Answers: D) 3, 3, 3, 3**

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Tags:- Perfect Square Series, Perfect Square, Square Series, Square, Perfect Series, Square Maths Series