Mathemagic #1 | How to find the square root of a number within 3 seconds (without using calculator)??

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What's up steemians...Welcome to the magical episode of Imagicnation ! A blog where we will reveal the answers to some of the most interesting & curious questions related to science...

Hey guys...Today, I'll be teaching you a secret trick which most physicist/mathematician often use but never share with their students ! It is actually a trick about how to find the square root of a square number within 3 seconds (without using calculator). So, are you excited?? Then here we go...

Suppose, take a number, say 3969.

Now, before starting the trick, we all must know about its basics, i.e, if a number ends with its unit digit 1, then the unit digit of its square will also be 1. 

Similarly:

For 2 it's 4, for 3 it's 9 and so on...

And, if you understood this we can now start solving some problems step by step. 

Step 1:

The first thing we need to do now is separate the given number (3969) into two parts, i.e, the RIGHT TWO DIGITS and the REMAINING DIGITS.

By that I mean to say: separate 3969 into 39 (REMAINING DIGITS) & 69 (RIGHT TWO DIGITS).

Now, our answer also comes in two parts _ _, (say A and B). 

(where A is the left digit of the ANSWER and B is the right digit of the answer)

The RIGHT TWO DIGITS gives the value of B while the REMAINING DIGITS gives the value of A.

Step 2:

So, to find the value of B we take the unit digit of RIGHT TWO DIGITS (69). So, here it is 9.

Now, from what we learnt from basics, we find out which are the numbers from 1 to 9 which when squared gives 9 at the unit place. So, they are 3 and 7.

Step 3:

To find the value of A we take the REMAINING DIGITS (39) and find out the biggest number whose square is smaller than 39. 

So, here that is 6 (since the square of 7 is greater than 39, we reject it)

Step 4:

Now, we now that the value of A is 6 and so we write 6 in the left side.

For the value of B we have to either select 3 or 7. So which should we select ??  See the final step for that.

Step 5:

Finallly, to find the value of B we do the following things:

i) Multiply A (i.e 6) with its next digit

-i.e, here 6 x 7 = 42

ii) Compare 42 with the REMAINING TWO DIGITS (i.e 39)

iii) Here, REMAINING TWO DIGITS (i.e 39) is smaller than 42. So, we select the smaller number, i.e from either 3 or 7.  Since, 3  is smaller is than 7,

Hence, the ANSWER WILL BE 63 !!

[Here, if the REMAINING TWO DIGITS was greater than 42, then we should select the greater number, i.e, 7.]

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So, BRAVO ! 

I hope you have understood the trick. But since it is new to you, you'll need a little bit of practice to answer in seconds.

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...& if you have really understood it then find the square roots of the following numbers and comment me as fast as you can.

5184 2809 1936 5476 6084

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