How to find a Square Root - A Shortcut Method

Friends, today we shall discuss the shortcut method for finding square roots. Lets start this post with some basic definitions.

What is Square Root ?

The square root of a number is any value when multiplied by itself, gives the number. Pretty simpler definition. Isn't it?

Now lets have a look at some examples

3x3 = 9 so the square root of the number 9 is 3

6 x 6 = 36 so the square root of the number 36 is 6

we represent square roots with the " √ " symbol.(Trust me its a square root symbol. Not a tick mark :P )

well, now we have a good idea of what is a Square root and how it looks like. Now lets come to our main topic.

 

How do you find Square Root ?

 

Well, its not such a complicated thing as you have been thinking.  Trust me, After reading this post you surely will be able to calculate square root of any number.

Before going to find the square root of any number, you should check whether the given number is a square or not.

Check the units place (right most digit) of the given number. If you find 2, 3, 7 and 8 at the unit place then we can say that the given number is not a square number and you can't find square root for the given number.

Ex : 652 is not a square number because there is 2 at the unit place of the number. 

The perfect square always ends with the numbers 1, 4, 5, 6, 9 and 0

(Update : this statement caused confusion to  a number of our readers. This doesn't mean all the numbers ending with the above mentioned values are square numbers). 

Now you have got a number to find its square root. Which is having one of these numbers 1, 4, 5, 6, 9 at the end. Now check the below table. Just try to remember it. Ofcourse, you easily can remember the values. Can't you ? :)

Unit’s Place	Factors
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	3 or 7
0	0

It simply says,

if the given number has 1 at the unit's place, then its square root will have 1 or 9 at the end (this is because 1x1 = 1 and 9 x 9 = 81)

if the given number has 4 at the unit's place, then its square root will have2 or 8 at the end (this ie because 2x2 = 4 and 8x8 = 64)

You know the logic behind 5

for 6, you will have 4 or 6 (4x4 = 16 and 6x6 = 36)

9, you will get 3 or 7 (3x3 = 9 and 7x7 =  49)

Ok, now come to the actual method of finding square roots of the given number.



Inorder to find the square root of the given number, you just should remember the following manthra. Just mug-up the following four lines.

1. Nearest Square
2. Its root          -----------> this will be the first number of our square root.
3. Its double
4. Join the factor and multiply with it --------> the factor will be the second number of our square root

Now lets see, how our table and manthra will help you finding square root of the number.

Assume that you should find out the value of  √2601

Given number is a square number (having 6 at the end). So we can find the square root of this number.

Step 1 : Take the Nearest Square of the first two digits of the number. Nearest square to the number 26 is 25 right?



Step 2 : Its root. (root of 25 is 5) -----------> First digit of our answer



Step 3 : Its double (double of 5 is 10)



now see, the below process,

Now, we have 101 at the reminder. You have nothing to do with the number. Just consider the ending number. Which is 1. According to our above table the factors of 1 are 1 and 9.

Step 4 : Join the Factor and multiply with it. For this step always try the smaller number, if it doesn't suits then only go with the larger number. Here in our case the smaller number is 1. So join it to 10. So it will become 101. Now multiply it with 1. We will get (101x1 = 101). So the second digit of the answer is 1.

So required square root is 51.

Lets have a look at another example,



Find the square root of 4096. 


√4096

Step 1 : Take the Nearest Square of the first two digits of the number. Nearest square to the number 40 is 36. 



Step 2 : Its root. (root of 36 is 6) ------------> this is the first digit of our required answer



Step 3 : Its double (double of 6 is 12)

Now, we have 496 at the reminder. Consider the ending number.
Which is 6. According to our above table the factors are 4 or 6.

Step 4 : Join the Factor and multiply with it. Try the smaller number, which is 4. Join it to 12 and it will becomes 124. Now multiply with the same number. 124x4 = 496. Which is our reminder.

So the second number will be 4.



So, 64 is the square root of the given number.

Note : If you cant get the required reminder while joining the first number, then simply join the second number. It will be your answer :)

Important Note : To make every step clear to understand, we have used these many steps. The process is very simple if you get the basic idea of it. So try to reduce the steps while working with this method.





That's all for now friends.Now try with some random examples. We shall discuss some more practice problems and the procedure to work with the bigger numbers in our next post. Please don't forget to review this method, please mention whether the way of explanation is understandable or not so that we can make further move. Happy reading :)