Squares and square root
If a number is multiplied by itself,the product so obtained is called the square of that number.
eg. 9 x 9 = 81, (3/7)2=9/49,
0.3 x 0.3=0.09
Properties:
(i) The square of an even number is always even. eg. (8)2=64
(ii)The square of an odd number is always odd. eg.(7)2=49
(iii) The number of zeros at the end of a prefect square is always even . eg. 20x20=400
(iv) If the given number has m digits, the square root will m/2 (m is even) or m+1/2 (m is odd)digit,
Conversely if the square root contains m digit,the square must consist of 2m or 2m -1 digits .
(v) Exact square can't end in 2,3,7,8.
(vi) A perfact square is never negative.
(vii) For any natural number m,
m2=sum of first m odd numbers.
eg. (5)2=1+3+5+7+9
(viii) If m is not a prefact square,then (m)1/2is not a rational number,it is irrational number.
eg. (8)1/2, (11)1/2, (17)1/2 etc.
(ix) If a number has 1 or 9(a complement from 10)
in the unit's place, then its square ends in 1.
(x) If a number has 4 or 6(a complement from 10)in the unit's place,then its square ends in 6.
(xi) If a number has 2 or 8 ( a complement from 10) in the unit's place, then its square ends in 4.
(xii) If number has 3 or 7(a complement from 10)in the unit's place, then its square ends in 9.
