# 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 :)

Krishna

1. Its amazing work mam/sir.
here after finding root is going to be simple.
thanks

1. i cant able to understand the factor steps. bit confusion. can any one clarify???

2. 4096 square root is 64 and also for 2601 is 51 then how could we use this??

1. There was a typing blunder friend. Corrected it. Hope everything is fine now :)

2. Thanx mam for the correction.. Nice post

3. square roots are 51 & 64.

4. This is Wrong !!! The Square root of 2601 is 51 and root of 4096 is 64.
what is this?

5. Nice post..... thnx

6. it's very interesting sir.......n very useful to solve the problem quickly.... after seeing this i 've tried in my own example of finding squareroot 1990 but i couldn't find the answer... so guide me in solving this .....

1. The number 1990 comes under exceptional case Poornima. Infact its not a perfect square.

2. shiv you mention in above i.e. perfect square end with 1,4,5,6,9,0 then plz clear...

7. Thanks A lot post this method finding very easy and
very short time please post another topic also

8. thank u....very nice
please give some english tricks for bank exam

9. can i tell easiest method for finding squareroot??

1. Ofcourse you can Karthic. YOu can mail us at "Gr8AmbitionZ(at)gmail.com"

2. Mast hai yaar thanks brother.

3. Mast hai yaar,. thanx bro

4. karthic bhai hume v thoda bataiye..mishra.sumeetkumar@gmail.com

10. Thank you..!!

11. Thanks for this...
Is there any shortcut to find square roots for above 4 digits number..

1. You can use the same technique by taking first 3 digits (for five digit numbers) and by taking first 4 digits for the numbers which are having more than 5 digits Teja. We will try to upload examples by tomorrow.

12. sir/mam.. pls upload study plan for ibps p.o. u told tht u will publish it today.. pls sir/mam.. hardly 2months r there.. we wont be able to follow it then.. pls upload the study plan as soon as possible.. thank u.

13. very interesting and simple.
though I would like to know more about the exceptions to 0.

1. We will try to arrange that by this weekend Rajeev.

14. post ibps po 3 study plan. I'm waiting for it.

15. thanx its gr8!

16. it is really good..thank..

17. Great
Many many thanks to Gr8Ambitionz

18. Thanks you are doing a great work..

19. No,its a wrong technique,its not working with all the numbers..
Tried for 2704,square root of 52....nearest square no.is 25 so we get the remainder as 204,and the unit digit is 4,double is 8,add and multiply it with either 2 or 8 i.e 82*2=164 and 88*8=704......and our remainder was 204.so how?

TRY IT FOR 2116 Square root of 46...will create the same problem and many no.'s like this.

So i request to the Admin team,delete this post and please look at the technique once more and correct it & post it.

1. You are little confused Friend. Please re read the post again. You have to double the root value of the first two numbers. Not the unit digit. In your case you have to double 5, then it will be 10. By adding and multiplying with 2, you will get 204. Which is your remainder.

So the root value 5 and the factor 2. The answer is 52

And in your second case also same,
Root value 4, and the factor 6 (doubling 4 you will get 8. Joining 6 and multiplying it with 6 you will get 516. Which is the remainder)

Hope it clear now. Please do comment if you still have problem with it.

20. useful...thank for d effort

21. Wonderful post. Thanks a lot...

22. Thanks for the post, its very useful.. can we consider all the numbers tat end with 1,4,5,9 are square numbers?

1. No friend. All that we tried to say was, The perfect squares always end in 1, 4, 5, 6, 9 or 00 etc. That doesn't mean all the numbers which are ending with these numbers are perfect squares (ex : 14, 15, 19 etc).

23. thanku mam

24. Thanks mam..its very useful&easy too..

25. Thank you soooooo much.... :)

26. PLEASE UPLOAD Some tricks for.......How to find the the square roots of 6 digit numbers???

27. thanks such a nice post

28. not working for all..say,root of 2304.for this,the nearest number considered acc. to u must be 25.and then it's root of 5 and it's double of 10 has to be taken and then the factors of 4(2 or 8) have to be considered.turns out that the square root of 2304 is 48.for that you have to consider 16 as the nearest no. to 23,which doesn't strike a bell to me as we all know 25 is far closer to 23 than 16...would appreciate if u explain this or am i missing something??

29. sir how take out square root of 144 by using this method

30. how to find 5 digit numbers square root like 33124?

31. sir,kindly justify this methord using 7 or 8 digit no.........suppose 1471369.

32. sir,kindly justify this methord for 7-8 digit no.....suppose 1471269

33. u showed only 4 digit how to do 3 , 5 and 6 digits ?

34. how to find square root of 18769

35. It didn't work for 2582449, that is square of 1607. Please check once?

36. Nathiya R
Perfect Explanation! Thanks a lot.

37. how to calculate sq root of 4489 ? as the nearest sq root of 44 is 7 and sq of 7 which is 49. 44-49 leaves remainder -5...can any one explain

1. The nearest sq root of 44 is 36

38. EXCELLENT .......... THANKS............IT REALLY WORKS

39. How to square root of 1256 & 2466 If Possible explain step by step

40. can we find sq. root of decimal number by this method?

41. Extra Ordinary.. having my MBA entrance exam in 3 days.. Dis was a life saver.. thnx a ton.. :D

42. Thanx a lot..THn .Finding Square root For Decimal number???

43. How can we find the square root of a number ends with using this method???

44. The method is very simple but i am not able to calculate for 5digit numbers(ex: 275625).Even if i consider the 1st 4 digits(2756) to find nearest square, how i ll know which is the nearest square number closer to this. It would be very helpful if u explain. Thank you.

45. can you plz find out the square root of 1331 from this method ?

46. how to find whether the number has root for some numbers that has no root but ending with 1,4,5,6,9,0

47. Lets try this Ex 1156.
Divide in to 2 parts as 56, 11
Hence 6 as ending 4/6
Now is nearest to 3x3=9
next letter of 3 is 4.
3x4=12
11 < 12
Hence 34
if obtained no is > 12 then 36

48. How should i calculate the square root 5 digit numbers

49. Okay. thats good..
Could you please give steps in getting square root for126376

50. Okay thats good..
could you please give the step wise solution for 126736

51. can you explain how to caculate square root of 921 and 9.87? i dont get how will you do it with that number

52. 2601^(1/2)
First divide the no. into 2 parts-1part with the units & tens place, other part with the rest of the no's
26 , 01
find the nearest square to 26 & find its root.
25 is the nearest sq. & 5 is its root
this 5 will be the 1st digit of our answer & our answer will be either 51 or 59 as 1 is the last no in 2601
We know 55^2 is 3025, hence the answer is less than 55