IRRATIONAL NUMBER
Any number √x (square root of x ) is an irrational number where x is a ‘+’ positive integers and x is not the square of a rational number.
There are some example is given below for your better understanding - 5 7
a) √2, √3, √5, √7, √11, √13, √5/7, √3/7, √7/11, √-------, √-------
11 13
are positive irrational numbers.
Similarly -√5, -√11, -√13, -√5/7, -√3/7, etc. are negative rational numbers.
But, we can conclude that, based on the logic following √64, √49, √81 are not suppose to be rational numbers because √64 = √8² = 8, √49 = √7² = 7, √81 = √9² = 9, that is 64, 49 & 81 are considered as a square of these 8, 7, & 9 rational numbers respectively.
b) The solutions of the equation a² = k are irrational numbers if k is not a perfect square.