Trick to find Square Root of Large Numbers

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)
12
1
22
4
32
9
42
16
52
25
62
36
72
49
82
64
92
81
102
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.
square root

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

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.

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. 

From the above diagram you can clearly see that before squaring and after squaring there is no change in unit place.
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

Point to Remember

While comparing if it shows that 84 is more than any other value then we will select 8 for unit place.

Must read

Shortcut trick to find Cube Root 
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