Short Tricks to find square of a 2-digit number

In this blog, I’ll tell you various strategies to find square of a 2 digit number in few seconds.

Strategy-1: Calculation based on distance

According to this strategy, 72 x 72 must be equal to 70 (that’s the original number minus the distance of 2) times 74 (that’s the original number plus the distance of 2) plus 4 (that’s the square of the distance of 2).

In other words,            72 x 72 = (70 x 74) + 4

Let’s do a couple of practice problems. I’ll start by showing you one more worked example, and then I’ll leave you to try the rest for yourself.

  1. 77 x 77 = 5,929The distance from 80 to 77 is 3, so 77 x 77 = (74 x 80) + 9 = (8 x 10 x 74) + 9 = (8 x 740) + 9 = 5,920 + 9 = 5,929
  2. 21 x 21 = _____
  3. 54 x 54 = _____
  4. 98 x 98 = _____

Strategy-2: For numbers ending with 5

The result of squaring any 2-digit number that ends with 5 starts with the number you get by multiplying the first digit of the number you’re squaring with the next highest digit and ends with the number 25.

For example, 35 x 35 must begin with the number 3 x 4 = 12 (since 3 is the first digit in 35 and 4 is the next number higher than 3) and ends with the number 25. The answer to 35 x 35 is 1,225.

Some  practice problems:

  1. 75 x 75 =_____
  2. 25 x 25 = _____
  3. 55 x 55 = _____
  4. 95 x 95 = _____

Strategy-3: Based on squares of numbers between 1 to 25

Let’s take example of 42

Step 1. In finding the last two digits of the answer, we shall find the square of the last digit of the number. Square the right-digit digit, which is 2 in this case. Hence we get 04

_ _04

Step 2. We shall now need to use the cross product. This is what we get when we multiply the two digits of the given number together. Multiply the two digits of the number together and double it: 4 times 2 is 8, doubled is 16: We write 16 as 6 and carry over 1 to the next step.

_ 64

Step 3: In finding the first two digits of the answer we shall still need to square the first digit of the number. That means we square the left hand figure of the number. Here square of 4 will be 16. Add 1 which is carried over from last step. Hence we get 16 + 1 =17

1764

That’s the answer.

Let’s try another example by squaring 64.

Square of 64 =     Square of 6 | double of cross product of both given digits 4 & 6| square of 4

Square of 64 =      36 |2x6x4 | 16

=      36 | 48 | 16

Collapsing the numbers

=      36 | 48 + 1 | 6

=      36 + 4 | 9 | 6

=      40 | 9 | 6

Hence the answer is 4096.

Learn more short tricks of Maths and Science

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