Chapter -5 Squares and square roots
Properties of square numbers
1. The numbers 1, 4, 9, 16, 25….are square numbers. Square of natural numbers are called perfect
square.
2. A number ending with 2,3,7 or 8 is never a perfect square.
3. If a number is ending with odd number of zeros than also it is not a perfect square.
4. If a number has 1 or 9 in its unit place then it’s square ends in 1.
5. If a number has 2 or 8 in its unit place then its square ends in 4.
6. If a number has 3 or 7 in unit place then it‘ s square ends in 9.
7. If a number has ‘n’ digit , than its square has (2n-1)or ‘2n’ number of digits.
E.g. square of 5 = 25
Square of 11 = 121
Square of 80 = 6400
Adding triangular Numbers
If we add two consecutive triangular numbers, we get a square number.
E. g 1+3 = 4 = 22, 6 + 3 = 9 = 32
Sum of consecutive natural numbers are triangular number.
Sum of n consecutive numbers = n(n+1)
2
Q- How many non-perfect square lie between 122 and 132
N =12 , n+1 = 13
No. of non- perfect square = 2xn = 2 x 12 = 24
NUMBERS BETWEEN SQUARE NUMBERS
We can say that there are ‘2n’ non – perfect square numbers between the squares of the
numbers ‘n’ and (n+1).
Adding odd numbers
Sum of the first n odd natural numbers is square of n
1[odd number]=1
1+3[Sum of two odd numbers =4] = (Square of 2)
Sum of first n odd number = (n2)
Eg 1+3+5+7
=n=4
