Rational numbers can be written as fractional form, a number which can be written as p/q format is rational number, 
a number which cant be written in p/q i.e in fraction form is called irrational numbers, 
rational numbers are 2/3,3/4
irrational numbers are root 2, root 3
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Rational numbers are real numbers which can be expressed as a ration of two integers, with the denominator being not zero.

Rational number =  n = p / q,  p and q are integers,  q ≠ 0.

examples are:  1, -1, -999999999.888232989 ,  1/3, - 0.987 / 0.56534,  87.67 / 98723, -7/2,

Rational number divided by or multiplied by a rational number is also a rational number.  All integers are also rational numbers.  Rational numbers can be added, subtracted, multiplied and divided - to get a rational number.

Irrational number is a real number which cannot be expressed as a ratio of two integers.  Some of these are square roots of integers which are not perfect squares or cubes.  

examples are:  ∛5 , ∛100,  √2, - √11  

Irrational numbers cannot be simplified by addition. √2+√5 cannot be simplified further.

We can have a lower bound and upper bound for the value of a rational number. If you have  
        a √2 + b√5 =  -3 √2 + 5 √5,  then a = -3 and b = 5

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