# CLASS-8IRRATIONAL NUMBER

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.