study material-mathematics

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

**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 7 ^{2}=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 8^{2}=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 4^{2}=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 5^{2}=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. 8 ^{2}=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: 1 ^{2}=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 2 ^{2}=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+3 ^{2} =25.**

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

**Step 7: Last step. 4 ^{2}=16.**

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