1. The extreme left column consisting of one to two digit numbers from 0 to 99.
2. Ten right columns containing one to six digit numbers , headed by the digits from 0 to 9.
* Note : From the identity, exact squares of four figure numbers can be easily calculated.
( x + y)² = x² + 2xy +y²
( x - y)² = x² - 2xy + y²
A Square table is shown below:
Solved examples using the table of squares :
1. Find the square of one digit number (i) 3² (ii) 5² (iii) 9² (iv) 8²
Solution : Easily find the square of one digit number and remember in mind.One digit numbers 1 to 9.
(i) 3² = 9 →Solution : Find the value of 3 by the using the squares table . Then we move horizontally to the right at the top of the column headed by 3 and the extreme left column consisting of number 0 read the figure 9. Therefore 3 squares is 9.
(ii) 5² = 25 →Solution : Find the value of 5 by the using the squares table . Then we move horizontally to the right at the top of the column headed by 5 and the extreme left column consisting of number 0 read the figure 25. Therefore 5 squares is 25.
(ii) 8² = 64 → Solution : Find the value of 8by the using the squares table . Then we move horizontally to the right at the top of the column headed by 8 and the extreme left column consisting of number 0 read the figure 64. Therefore 8 squares is 64.
(iv) 9² = 81 →Solution : The extreme left column consisting of number 0. Right columns containing read two digit number 81, headed by the digits 9 .Therefore 9 squares is 81.
2. Find the square of two digit number Quickly find the square of two digit number using squares table . Two digit numbers 10 to 99.
For example ⇒
(i) 10² = 100 →Solution :Determine the value of squres easily find the square of 10 using the squares table. The extreme left column consisting of number 1. Then we move horizontally to the right at the top of the column headed by 0 and Right columns containing read three digit number 100.
(ii) 12² = 144 →Solution : Determine the value of squres easily find the square of 12 using the squares table. The extreme left column consisting of number 1. Then we move horizontally to the right at the top of the column headed by 2 and Right columns containing read three digit number 144.
(iii) 15² = 225 →Solution : Find the value of squres easily find the square of 15 using the squares table. The extreme left column consisting of number 1. Then we move horizontally to the right at the top of the column headed by 5 and Right columns containing read three digit number 225.
(iv) 98² = 9604→Solution : Determine the value of squres quickly find the square of 98 using the squares table. The extreme left column consisting of number 9. Then we move horizontally to the right at the top of the column headed by 8 and Right columns containing read four significant figure number 9604.
3. Find the square of three digit number quickly find the square of three digits numbers using squares table . Three digits numbers 100 to 999.
For example ⇒
(i) 103² = 10609 →Solution : The extreme left column consisting of number 10. Then we move horizontally to the right at the top of the column headed by 3 and Right columns containing read five digit number 10609.
(ii) 121² = 14641 →Solution : The extreme left column consistingSolution of number 12. Then we move horizontally to the right at the top of the column headed by 1 and Right columns containing read five digit number 14641.
(iii) 125² = 15625 → Solution : The extreme left column consisting of number 12. Then we move horizontally to the right at the top of the column headed by 5 and Right columns containing read five digit number 15625.
(iv) 888² = 788544 → Solution : The extreme left side column consisting of number 88. Then we move horizontally to the right at the top of the column headed by 8 and Right columns containing read six significant figures 788544.
(v) 987² = 974169 → Solution : The extreme left side column consisting of number 98. Then we move horizontally to the right at the top of the column headed by 7 and Right columns containing read six significant digits 974169.
****************************************
