How to Quickly Calculate Square of Three Digit Numbers?

Learn to Quickly Calculate Square of Any Three Digit Number

The method of squaring any 3 digit number is an extension of my last post on finding square of any two digit number. To understand and appreciate squaring of 3 digit numbers you should be well versed with shortcut of squaring any 2 digit number. Let us start learning this with the help of an example.

What is the square of 384?

Step 1: To begin with ignore the 3 of 384. You are left with only 84, a two digit number. Using the method of squaring 2 digit numbers, find the square of 84. We get the answer as

Square of 8  |   twice of 8 X 4   |  square of 4

64            64           16

7056 (consolidating the result obtained above)

Step 2: This step is new and different from what we’ve learned in the previous post for squaring 2 digit numbers. Watch carefully.

We have to multiply the first and last digits of our original number and double it. Essentially, that is multiplying together 3 and 4 and then doubling it. Hence we get 24.

Add this number directly to the two left hand digits of our number obtained from the first step.

7056

Add 24 to 70. 70+24=94. So 7056 gets converted to 9456.

Step 3: In the first step we left out the first digit of our number and squared the last two digits. Now we will forget about the unit’s digit 4 and square the first two digits i.e. 38 as before just omitting to square the last digit 8.

Square 38 as a regular 2 digit number, except that you omit the 8 squared.

Square of 3 | twice of 3 X 8

9       |   48

Step 4: Consolidating this with the result obtained in step 2,

9   |  48   |  9456

14        7       456

Hence the answer is 147456.

I’ve shared this method of squaring 3 digit numbers as an extension to the shortcut of squaring 2 digit numbers. Initially you might feel that the traditional method is quicker than having to memorize and execute these steps. However, this method can prove to be quicker than the useful one only if you master this technique with lot of practice.

Do you think this method will help you in reducing the time to calculate square of 3 digit numbers?

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How to Quickly Calculate Square of Any Two Digit Number?

In this post I’ve tried to improvise on the method of squaring presented in one of the earlier posts on Quickermaths.com itself. This trick of squaring any two digit number with ease is inspired by squaring techniques from the book – The Trachtenberg Speed System of Basic Mathematics

I would like to explain this method of squaring any 2 digits number with the help of an illustration.

What is the square of 32?

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: 3 times 2 is 6, doubled is 12: We write 12 as 2 and carry over 1 to the next step.

_ 24

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 3 will be 9. Add 1 which is carried over from last step. Hence we get 9 + 1 =10

1024

That’s the answer.

This method can also be compared with another shortcut to find the square of any number posted by me on Quickermaths.com in the past.

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.

Have you come across any other squaring method like this?

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Squaring any 2-digit number

A guest post by Maria Rainier

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. Read More

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Shortcut to Find Square of a Number

Today I will discuss a very simple method of finding square of numbers between 26 to 74 mentally. In the subsequent post we will cover higher numbers. So keep watching this space to learn squaring any number within your mind

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. Read More

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How to Quickly Find Square of Any Number Ending in 5

Finding square of any number with unit’s digit being 5 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.  Also explore a quick method of squaring numbers ending in 9. Given below is the step by step explanation of this Vedic Maths Method.

Let us take a 2 digit number in generic form, say the number is a5 (=10a+5), where a is the digit in ten’s place

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

That means a is multiplied by the next higher number, i.e. (a+1). Now let’s take example of a real number ending in 5, say 45.

452 = Left hand side of the answer will be 4 multiplied by its successor i.e. 5 and the right hand side part will always be 25 for squares of numbers of which the unit’s digit is 5.

Giving the answer a x (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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