**Perfect Square Series**

Perfect square series is a arrangement of numbers in a certain order, where some numbers **Series are based on square of a number which is in same order you need to place one square number that is missing in that given series, **we need to observe and find the accurate number to the series of numbers.

This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. It is simple to work on perfect square root numbers you can easily obtain the result of perfect square number. How you get easily by Perfect square numbers missing term by memorize square and square root numbers shortcut tricks .

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.

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 its square roots are always integers positive numbers. so For example, √4 = ±2, so 4 is a square number.

**Perfect Square Series**

Here we see the some examples that how the perfect square are arranged how the missing square series are arranged.

**Example 1:** 841, ?, 2401, 3481, 4761

**Answer :** 29^{2}, 39^{2}, 49^{2}, 59^{2}, 69^{2}

**Example 2:** 1, 9, 25, ?, 81, 121

**Answer :**** **1^{2}, 3^{2}, 5^{2}, 7^{2}, 9^{2}, 11^{2}

**Example 3:** 289, 225, 169, ?, 81

**Answer:** 17^{2}, 15^{2}, 13^{2}, 11^{2}, 9^{2}

**Example 4: ** 441, 484, 529, 576, ?,

**Answer:** 441 = 21^{2}, 484 = 22^{2}, 529 = 23^{2}, 576 = 24^{2 },625 = 25^{2}.

**Example 5: ** 121, 144, 169, ?, 225

**Answer:** 121 = 11^{2}, 144 = 12^{2}, 169 = 13^{2}, 196 = 14^{2}, 225 = 15^{2}.

**Example 6:** ?, 2116, 2209, 2304, 2401, 2500

**Answer:** 2025 = 45^{2}, 2116 = 46^{2}, 2304 = 48^{2}, 2401 = 49^{2}, 2500 = 50^{2}

**Example 7:** 961, 1024, ?, 1156, 1225

**Answer:** 961 = 31^{2}, 1024= 32^{2}, 1089 = 33^{2}, 1156 = 34^{2}, 1225 = 35^{2}.

**Example 8:** 36, ?, 64, 81, 100, 121

**Answer:** 36 = 6^{2}, 49 = 7^{2}, 64 = 8^{2}, 81 = 9^{2}, 100 = 10^{2}, 121 = 11^{2}.

**Example 9:** 121 , 169 , ? , 289 , 361

**Answer :** 11^{2} = 121 , 13^{2} = 169 , 15^{2} = 225 , 17^{2} = 289 , 19^{2} = 361.

**Example 10:** 121 , 484 , 1089 , 1936 , ? , 4356

**Answer :** 11^{2} = 121 , 22^{2} = 484 , 33^{2} = 1089 , 44^{2} = 1936 , 55^{2} = 3025 , 66^{2} = 4356.

**Example 11:** 961 , 1024 , 1089 , ? 1225

**Answer :** 31^{2} , 32^{2} , 33^{2} , 34^{2} , 35^{2}

**Example 12:** 1849 , ? , 2025 , 2116 , 2209

**Answer :** 43^{2} , 44^{2} , 45^{2} , 46^{2} , 47^{2}

**Example 13 :** 2500 , 2401 , 2304 , ? , 2116 , 2025

**Answer :** 50^{2} , 49^{2} , 48^{2} , 47^{2} , 46^{2} , 45^{2}

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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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