Squaring NumbersSomething, most of us get stumped at is finding the square of numbers. While we can remember square of 1-digit numbers easily and even certain 2-digit numbers like 10, 11, 12 and 13 due to repeat usage, but what to do about other numbers? We certainly cannot sit and memorize the square of all the other 2-digit numbers. So, here we present to you a quick fix to the problem of finding the square of 2-digit numbers.

Trick to Find Squares of a number

  • Step 1: Identify the number whose square we need to find.
  • Step 2: Find the difference between the identified number and its nearest 10s number.
  • Step 3: Add and subtract the answer of Step 2 to the number identified in Step 1. We obtain 2 results in this step.
  • Step 4: Multiply the two numbers obtained in Step 3
  • Step 5: Square the result obtained in Step 2.
  • Step 6: Add the result of Step 5 to the result of Step 4 to get the final answer.

Let us try…

Now, that we have detailed the steps of the trick, we should try using it to find squares of some numbers. Let us find the square of number 23.

Step 1: Identify the number whose square we need to find.

Step 1

Step 2: Find the difference between the identified number and its nearest 10s number.

The nearest 10s number to 23 is 20 and the difference between them is 3.

Step2

Step 3: Add and subtract the answer of Step 2 to the number identified in Step 1.

Untitled

Step 4: Multiply the two numbers obtained in Step 3.

Step 4

Step 5: Square the result obtained in Step 2.

Step 5

Step 6: Add the result of Step 5 to the result of Step 4 to get the final answer.

Step 6

Here is the final answer. The square of 23 is 529.

Let us try once again

This time, let us try this trick on a more challenging number. 66 sounds real tough one.

Step 1: Identify the number whose square we need to find.

66-1

Step 2: Find the difference between the identified number and its nearest 10s number.

The nearest 10s number to 66 is 70 and the difference between them is 4.

66-2

Step 3: Add and subtract the answer of Step 2 to the number identified in Step 1.

66-3

Step 4: Multiply the two numbers obtained in Step 3.

66-4

Step 5: Square the result obtained in Step 2.

66-5

Step 6: Add the result of Step 5 to the result of Step 4 to get the final answer.

66-6

Here is the final answer. The square of 66 is 4,356.

Things to note to Find Squares of a number

  1. The most difficult part of this trick is the step 4. While it may seem easy during the 20s and 30s, but the math grows complex as we approach the larger numbers. Therefore, make sure to practice your multiplication skills well if you plan to use this math trick. A great and easy way of practicing multiplication skills is through math games.
  2. For first few times, practice this trick on paper. Resort to mental calculations only after you have mastered the steps. Practicing on paper will also ensure that you get your step 4 multiplication right.
  3. This trick has made use of the number flexibility of finding the nearest 10s number. Multiplying any number with a 10s number is always easy because all you do in that case is multiply the number with the tens digit and add a ‘0’ to the result.

This squaring trick can be of great help during competitive exams or solving geometry questions which often involves a lot of squaring. Hope you find this trick helpful and make sure that you revisit the trick and practice it often so that it sinks into your brain and becomes a part of everyday math.