Trick Alert: Fastest way to find the square of any two digit number in mind.

Hey again!

Today, I will show you how to quickly find a square of any two digit number in mind. There are few cases here. Let’s begin.

Case I: Numbers ending with zero.

This is rather an easy one. Let’s take a two digit number say 50. Since, this number ends with a zero “0”, its square will end with double zero “00”

x0^2 = xx00

Now, take the square of first digit, i.e., 5^2 = 25 and prefix it to the two zeros.

50^2 = 2500

Similarly,

70^2 = 4900


90^2 = 8100

Case II: Numbers ending with 5.

Let’s take 35 in this case. When, number is ending with “5”. its square will always end with “25”. Thus,

x5 ^ 2 = xx25

Now, take the first digit i.e., 3 and multiply it by next consecutive integer i.e., 4,

3 x 4(Next Integer) = 12

Now, prefix this product to “25”. Therefore,

35 ^ 2 = 12 25

Similarly,

55 ^ 2 = 30 25


75 ^ 2 = 56 25

Case 3: Square of any other two digit number.

Let’s take 99 this time. You need to find closest number to 99 that can easily be multiplied in mind. For me, and I am sure, for most of you, its 100. Your goal is to reach to 100. To do this you have to add “1” to 99. But, it’s law of nature, you have to give back what you take. So, you also have to subtract “1” from 99. It should look like this.

98    =    (-1)    99    (+1)    =    100

Now, we have got two numbers, 98 and 100. To get the square of 99, you need to multiply these two numbers (i.e., 98 and 100) and add to it the square of incremental value like this:

99 ^ 2 = 98 x 100 + (1)^2

9800 + 1

9801

Try your hands on these problems and try to solve them in mind.

  • 30^2
  • 80^2
  • 15^2
  • 95^2
  • 21^2
  • 42^2

I hope you understood and will apply this more often in your calculations. Happy calculating :).

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