In Quantitative Aptitude, time is the biggest constraint. We always try to find ways and techniques to save time. By **finding Square Root of any number**, you easily save few minutes during the exam. It can act as the** game changer** during the competitive exams.

Lets know about the Trick

### Perfect Square Root of four digits numbers within 4 to 6 seconds

First of all you should have the knowledge of square root of 1 to 10. From the below given diagram you can easily understand it.

Square Root (1 – 10) | |
---|---|

1^{2} | 1 |

2^{2} | |

3^{2} | 9 |

4^{2} | 16 |

5^{2} | 25 |

6^{2} | 36 |

7^{2} | 49 |

8^{2} | 64 |

9^{2} | 81 |

10^{2} | 100 |

### Rule 1

1 comes in unit place if you square 1 or 9 only. In simple words we can say that when we have to find the square root of 1 then answer will be 1 and if we have to find the square root of 9 then answer will be 81 means in unit place 1 exists. Only after squaring 1 and 9 we get 1 in unit place of particular digit.

6 comes in unit place if you square 4 or 6 only. In simple words we can say that when we have to find the square root of 4 then answer will be 16 and if we have to find the square root of 6 then answer will be 36 means in unit place 6 exists. Only after squaring 4 and 6 we get 6 in unit place of particular digit.

### Rule 2

4 comes in unit place if you square 4 or 8 only. In simple words we can say that when we have to find the square root of 2 then answer will be 4 and if we have to find the square root of 8 then answer will be 64 means in unit place 4 exists. Only after squaring 2 and 8 we get 4 in unit place of particular digit.### Rule 3

9 comes in unit place if you square 3 or 7 only. In simple words we can say that when we have to find the square root of 3 then answer will be 9 and if we have to find the square root of 7 then answer will be 49 means in unit place 9 exists. Only after squaring 3 and 7 we get 9 in unit place of particular digit.### Rule 4

### The Value whose unit place never changed ( 5 and 0)

- If you find square root of those values whose unit place is 5 or 0 then in the answer unit place will be same as previous.

Lets understand the tricks with examples.

### Square Root of 4 Digit Numbers

**Q1. Find the square root of 8464?****Solution**

**First Step (Make the Pairs and Check the Unit Place)**

- Make the pair of 8464 such as 84 and 64
- 4 is in the unit place of 8464. It means in square root value, unit place will be 2 or 8 as we discussed above.

**Second Step (Leave Last 2 Digits)**

- Now we have to work on 84. Square of 9 is 81 and square of 10 is 100. So, 81 is near 84. Now we can select 9 for tens place in answer.

**Third Step (Multiply the successor of selected tens place item)**

- As we know 9 is selected for tens place in answer but now we have to find the unit place in answer it may be 2 or 8.
- Now multiply the 9 with its successor i.e. 10 then answer will be 9
**×**10 = 100. Now compare the 100 with 84. 84 is less than 100. Comes towards the unit place value that may be 2 or 8. It will be 2 because 84 is less than 100. So answer is**92**.

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