Shortcut to Squaring Any 2-Digit Number

What do you do when your calculator has been confiscated and the world is depending on you to square a two-digit number within a minute? Don’t panic – just follow three simple steps that require basic addition and multiplication, and you’ll be able to solve the problem in no time. If you practice enough, you’ll even be able to complete each step mentally, rendering scratch paper unnecessary. This will save you time on drills and strengthen your skills so you can tackle other challenges. Eventually, you’ll be able to solve multi-step squaring problems without ever breaking a sweat – or a pencil.

This is a trick I learned during my old MATHCOUNTS days, but it comes in handy for lots of other competitive math as well. It was great for sprint, team, target, and countdown problems, but now it just comes as second nature whenever I run into a more complex problem that involves a squaring step. If you’re having trouble squaring two-digit numbers on the fly without a calculator, give this method a try. It seems a bit cumbersome at first, but as you practice, you’ll be able to speed up the process and get your answer within seconds.

3 Steps for 2-Digit Squares

Let’s work through the steps with an example to better demonstrate the process. Imagine that you’re expected to square 83 quickly and accurately – the following steps will help you complete the task.

1. Square each digit individually, making sure that you get a two-digit number for each square. If the number is low and its square gives you only one digit, use 0 as a placeholder.

8² = 64 and 3² = 9 = 09, giving you 6409

2. Now, multiply the two digits and double your answer, adding a 0 to the end.

8 X 3 = 24; 24 X 2 = 48, giving you 480

3. Simply add your answers from steps one and two.

6409 + 480 = 6889, or 83²

Bio: Maria Rainier is a freelance writer and blog junkie. She is currently a resident blogger at First in Education, where recently she's been researching different online mechanical engineering degree programs and blogging about student life. In her spare time, she enjoys square-foot gardening, swimming, and avoiding her laptop.

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3. Squaring number ending in five : Vedic Maths Trick

Square (also called perfect square) is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.

How to find the square of any number?

To apply this method you should know squares of 1 to 25 by heart. You can refer to this table to learn the same.

For finding square of any number between 26 to 75

Step 1. Find the difference between 50 and the number you want to square.

Scenario 1: If the number to be squared is greater than 50

Step 2. Add that many 100s to 2500 (which is the square of 50)

Step 3. Then add the square of the difference to the result of step 1

Scenario -2: If the number is less than 50

Step 2. Subtract that many 100s to 2500.

Step 3. Then add the square of the difference to the result of step 1

Example

Find out the Square of 67.

Step 1. Difference of 67 and 50 = 67-50 = 17
Step 2. This number is greater than 50. So add 1700 to 2500 = 4200
Step 3. Add square of 17 to step 2.

Answer = 4200+ 289 = 4489

Alternative method of calculating the square of a number:

Since, 67-50 = 17

67^2

We will be getting answer in 2 parts; see below – right hand side gives you tens and units digit. Left hand side gives you the remaining digits.

= 25 + 17 | (17)^2 ( | denotes separation )

= 42 | ₂89 (17^2 is 289. The 2 shown in subtext will be carried over and added to left hand side)

= 4489

Related posts:

1. Base Method of Multiplication
2. Trick to Find Square of Numbers from 51 to 59
3. Vedic Multiplication of two numbers close to Hundred

This is the most common, yet very interesting trick of Vedic Maths.  Using this technique you can find the square of any number ending in 5 very easily.  Given below is the step by step explanation of this Vedic Maths Method

Let us take a 2 digit number,

Say the number is a5 (=10a+5), where is the digit in ten's place

Square of a5= a x (a+1) | 25

For example,

45² = (40 + 5) ², It is of the form (10a+b) ² for a = 4

Giving the answer a (a+1) | 25 ( |     stands for concatenation}

i.e. 4  x  (4+1) | 25 = 4 x 5 | 25 = 2025

Similarly we can proceed for 3 digit numbers ending in 5

Few more examples:

95²= 9 x 10 | 25 = 9025

125² = 12 x 13 | 25 = 15625

505² = 50 x 51 | 25 = 255025

Test yourself

Find out the square of 85, 245, 145, 35, 15, and 95?

Answer: 7225, 60025, 21025, 1225, 225, 9025

Please let us know if you like this Vedic Maths trick

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1. Vedic Multiplication Trick
2. Finding Cube Root – Vedic Maths Way
3. Speed Multiplication by 111 : Vedic Maths