How To Find The Square Of Any Number Quickly!! [A must have tool for IIT-JEE and AIEEE]

6 Sep 2008

I will explain an easy way of finding the square of a number (any number of digits.)

I will explain for 2, 3 and 4 digits numbers.

Example 1:

Two digits: 78

First square seven 7²=49

Write it down.

Then you multiply the both digits and make it double, 7*8*2=112

Write it down. (I will show how to write it.)

Now the next digit 8.

Square it 8²=64 (I will show how to write.)

Just see the image at the bottom of the page.

Easy………..

Now a three digit number.

Now a three digit number.

Example: 458

Step 1: Square the first digit 4²=16

Step 2: The next two digit 4 and 5. Multiply together and double it. 4*5*2=40

Step 3: Now take all the digits multiply 4 and 8 and double it and add 5²=25 to it. We will get

(4*8*2)+25=89.Write it as shown,

Step 4: the next two digits including 5. 5 and 8. Multiply together and double it. 5*8*2=80

Step 5: The last digit 8. Square it and write it down. 8²=64.

So we end all the calculations and here comes the trick to write it.

I will make it shorter.

First take the first digit and square it.

Then take the next two digits and do as mentioned.

Then take all three digits together and do as mentioned.

Then leave the first digit and take the last two digits.

Then leave the first two digits and take the last digit and do as mentioned.

Ok now for four digits!!!

You may think that it would be complicated. But if you find 5-6 squares with it then it becomes really easy!!!

For Four digits...........

Example: 1234

Step 1: 1²=1 write down.

Step 2: Consider 1 and 2. Multiply and double it. 1*2*2=4

Step 3 : Now consider 1,2 and 3. Do the Step 3 for a 3 digit number. Multiply 1 and 3 and double it. 1*3*2=6. Add 2²=4 to it. So it becomes 10.

Step 4 : Now consider 1,2,3 and 4. multiply 1 and 4 and double it.1*4*2=8. Now multiply 2 and 3 and multiply it and double it. 2*3*2=12 add them. 8+12=20.

Step 5: Now 2,3 and 4. (Same as step 3.......) 2*4*2+3² =25.

Step 6: Now 3 and 4. Multiply and double them. 3*4*2=24.

Step 7: Last step. 4²=16.

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