Squaring Numbers close to 50

Here is a nifty trick to square numbers close to 50 ranging from 30 – 70 (ranges vary at capacity) at extremely fast speed.

In order to find the square of any number closer to 50, all we need to do is,

• Step–1:        Find out how much more or less than 50 is that number i.e. the distance of that number from 50.

• Step–2:        Add that distance to 25 if the number to be squared is above 50, or subtract the distance from 25 if the number is below 50.

• Step–3:        For the last 2 digits, find the square of that distance. If it is a single digit answer, make sure to put an extra ‘0’ before it to make it a 2 place. If it is a 3-digit answer, carry forward the left digit.

Let’s illustrate with example, 57² =?

1)   57 is 7 more than 50.

2)   Add 7 to 25. 25 plus 7 is 32.

3)   For the last 2 digits, find the square of that distance i.e 7. Square of 7 is 49. So, put 49.

So, 57² =3249

53² =?

1)   53 is 3 more than 50.

2)   25 plus 3 is 28.

3)   Square of 3 is 9. So, put 09.

So, 53² =2809

See the pattern?

So, 62² =?

1)   62 is 12 more than 50.

2)   Add 12 to 25 to get 37.

3)   Square of 12 is 144. Put 44 to the last 2 places and carry forward 1 to 7. 7 plus 1 is 8.

So the answer is 3844.

Now, what if the numbers which you are trying to square is less than 50? This is the same technique. Just subtract the distance from 25.

Let’s say 47² =?

1)   47 is 3 less than 50.

2)   Subtract this distance from 25. 25 minus 3 is 22.

3)   Square of the distance i.e. 3 is 9. So, put 09.

 So, 47² =2209

42² =?

1)   42 is 8 less than 50.

2)   25 minus 8 is 17.

3)   Square of 8 is 64.

So, 42² =1764

37² =?

1)   37 is 13 less than 50.

2)   25 minus 13 is 12.

3)   Square of 13 is 169. Put 69 and carry forward 1 to 2. 2 plus 1  is 3.

  

So, 37² = 1369