Square root in 3 sec

In this post, Study Buddy is introducing a very fast way of finding square root of any perfect square less than 10000 quickly. 

Note: Don't be discouraged by the long text. The steps can be done in seconds and can actually be written in one sentence but it is written long for the purpose of explanation and for the clarity of the content for all kinds of readers. Also I will give you some homework questions for you to try and solve some square root problems on your own to speed up the process. If you learn this method, finding square roots will be piece of cake for you. So take the time to read it completely.

Let's take a number, say 3481

Can you find the square root of this number easily? 

But I can do it in 2-3 seconds knowing only squares of 1-10 and I will tell you exactly how this trick goes. 

Here is the algorithm

Example 1: 3481

1. The square root of any number between 100-10000 will be a two-digit number. Take a look at the last digit of the number and find the 2nd digit of the square root. Unless the last digit of the number is 5, you'll have two options to chose from.  Check this table below. If you observe, squares of numbers ending with 4 and 6 end with 6. You have probably known this already. Otherwise you'll digest it over time. The first step is this. What we have is the number 3481. Last digit of this number is 1. So the last digit of the square root is either 1 or 9 as it is clear from the table.    
   
                                                                    
2. The second step is to remove the last two digits of the number and consider the first two digits. Eg: If it is a 3 digit number like 576, remove last two digits (5 76) and take 5. If it is a four digit number like 1024 remove 24 (10 24) and take only 10. We don't want the last two digits in the second step. In 3481, we will remove 81 and take only 34 in this step. Then think about the squares from 1-10 and figure out in which interval does 34 belong in the squares table. Of course, it is between 25 and 36 which are squares of 5 and 6. Since 34 lies between the squares of 5 and 6, the first digit of the square root as 5. Or in other words, the biggest square less than or equal to 34 is 25 which is the square of 5. 2nd step is complete. We have two answers before us which are 51 and 59. How to find out which one is correct?      
   
                                                                   
3. In the third step, we need to identify the last digit from the two choices. If the last digit is 5, we don't need this step.For that we will take the first digit of the square root we found out in step 2 which is 5. This step is a bit tricky but read carefully and you'll understand it well. We should multiply 5 with the next number 6. 5 times 6 is 30 (5x6=30). Compare the first two digits in our question with 30. If the first two digits of given number is greater than the number obtained by multiplying, we should take the bigger digit. Otherwise take the smaller digit. 34 is the first two digits in the question. 34 is greater than 30. So we'll take the greater option from 1 and 9 which is obviously 9. 

I don't expect everyone to understand the 3rd step in the first attempt. We'll do another simpler example.

Example 2: 484

Step 1: the last digit of square root is 2 or 8 because the last digit of the given number is 4.

Step 2: 484 Strike the last two digits and find the biggest square less than or equal to 4. From the Table 2 we know that biggest square less than or equal to 4 is 4 itself and 4 is the square of 2.

So we take 2 as the first digit.

Two options: 22 and 28

Step 3: Take the first digit ie. 2 and multiply it with next number 3

2x3=6. Removing last two digits of 4 84 , we have 4.

4 is less than 6. So we take the smaller option from the two ie  2

Square root of 484 is 22.

Last example: 1225

Step 1: Last digit of square root is 5 because last digit of  the 1225

Step 2: Remove 25. (12 25). Biggest square root less than or equal to  12 is 9. Square root of 9 is 3.

First digit is 3.

Square root of 1225 is 35

Practice Questions:

• 225
• 729
• 3364
• 3721
• 1024
• 2025
• 2401
• 7569

If you have any doubts regarding this, don't hesitate to ask in the comments.