Lesson10

Lesson10
Squares

Finding square of any number is very very easy and you can calculate it very fast But before
going to concept ,you should do some home work . You are well conversant in squaring of
1 to 9
1x1 =1
2x2 =4
3x3 =9
4x4 =16
5x5 =25
6x6 =36
7x7 =47
8x8 =64
9x9 =81
These are square from 1 to 9 . Now learn square index of 1 to 9
Number Square Index Operation
1 2 First digit
squaring
1 to4
Multiply first
digit to next to
first digit
5 to9
2 4
3 6
4 8
5 0
6 2
7 4
8 6
9 8
Square Index is nothing except table of 2 .We just double
number in first part ie from 1 to 4 and leave ten 's digit in
second part ie from 5 to 9 after doubling .
Steps Now learn main concept by this example
21 x21 =????
Here our last digit (or unit digit ) is1 .Its square index
is 2 First we take square of 1 and write it extreme right then
we take first digit and multiply it by the square index write before
last figure then squaring first digit and write extreme left
If there is any carry add to it
1x1 =1 2x2 =4 22 =4 4 4 1 Answer
44 X44=????
Here square index of 4 is 8
4x4 = 16 4x8 +1(carry ) =32 +1 = 33 42 + 3 =16+3 =19 1936 Answer
93 X93 =????
Here square index of 3 is 6
3x3 =9 9x6 =54 92+ 5 =81 +5 =86 8649 Answer
These are the square where last digit is 1 to 4 now we learn squaring of those numbers
having last digit from 5 to 9.Method is same, instead of squaring first digit multiply to
next digit
36 X36 =
Here square index of 6 is 2
6x6 =36 3x2 + 3 =6+3=9 6X(6+1) = 6 x7 =42 42 96 answer
87 x 87 =
Here square index is 4
7x7=49 8x4+4 =32+4 =36 8x(8+1)+3 =72+3 =75 75 69 Answer
25x25 =
Here square index is 0 so no need of middle step
5x5 = 25 2x(2+1) = 6 625 answer
Now with the help of this concept we can calculate square of any number
236 x 236=????
Here square index of 6is 2
6x6 = 36 23 x2 +3 =46+3=49 23x24*+4 =552+4=556 55696 answer
*23x24 = ? By cross and vertical multiplication method(covered in lesson no 7)
4 / 14 /12 = 552