Square of a number – Part 1

We have seen how to do multiplication using vedic maths, there are still some more topics balance in multiplication but in this post I want to teach about finding square of a number.

What is square of a number?

Any number multiplied by itself is called square of that number.

Square of number X is written as X² and is called X square.

Some simple squares:

1² = 1× 1= 1

2² = 2× 2= 4

3² = 3× 3= 9

4²= 4× 4 = 16

5² = 5× 5= 25

6²= 6× 6= 36

7² = 7× 7= 49

8² = 8× 8= 64

9² = 9× 9= 81

10² = 10× 10= 100

Square of number from 11 to 19

Let us write a formula to find square of number from 11 to 19.

Here we are taking 10 as base.

Let us take number ab, square of number ab= ab² = (ab+ b) \ b²

Let us take examples now

Example1: 11² = (11+ 1) \ 1² = 12\ 1= 121

12² = (12+ 2)\ 22= 14\ 4= 144

19² = (19+ 9) \ 9² = 28\ 81, in this case number in the right side is 2 digit so we have to carry 8 to left side

= 28+8\ 1= 361

Practice:

1) 13²

2) 14²

3) 15²

4) 16²

5) 17²

6) 18²

Square of 20 is easy to find 20² = 20× 20= 400

We will come back to square of number from 21 to 24 later, first we will find square of 25.

Square of any number ending with 5

To find the square of any number (a5) = (a5)² = (a× (a+1)) │5² = (a× (a+1)) │25

 

Let us take an example 25² = (2× (2+1)) │ 5²

= (2× 3) │25 = 625

So 25² = 625

Let us take one more example 45² = (4× (4+1)) │ 5²

=4× 5 │25

45² =2025

Practice:

1) 35²

2) 55²

3) 95²

4)105²

5)115²

Square of an adjacent numbers

Some squares are easy to find example 25²,30², 40²,50², 60²  but what about finding squares of 24,26, 29, 31, 39, 41, 49, 51, 59, 61 so on ….. If you check these numbers you will find these numbers are adjacent to the number whose square is easy to find.

Adjacent number can be one above or one below.

Number below easy numbers:

Let us take number (ab-1).

(ab-1)² = ab² – (ab + (ab-1))   , Here ab is a number whose square is easy to find.

Let us take example to explain how to solve this.

24² = 25² – (25+ 24)

= 625- (25+ 24) = 625- 49

=576

Let us take one more example.

49² = 50² – (50+ 49)

=2500- 99

=2401

Practice:

1) 74²

2) 39²

3) 29²

4) 49²

5) 59²

Number above easy numbers:

Let us take number ab+ 1.

(ab+ 1)² = ab² + (ab+ (ab+ 1))

Let us take an example

36² = 35² + (35+ 36), we have already studied how to find square of number ending with 5.

= 1225+ 71

= 1296

Take one more example

81²= 80² + (80+ 81)

= 6400+ 161

= 6761

Practice:

1) 31²

2) 46²

3) 56²

4) 41²

5) 71²

There is much more to learn about finding square of a number, we will cover this in the next post. Keep reading.