The number which cannot be written as simple fraction or which is not in form p/q is called irrational number. In simple words, a real number that is not a rational number is known as irrational number. The first irrational number, which discovered is Square root of two. The value of √2 is 1.41421.....The other example of irrational number is pi and the value of pi is 3.147……. In this irrational number the value is not repeated. The types of irrational number are Algebraic Numbers and transcendental numbers. These two types of irrational number are explained one by one. Firstly the algebraic numbers are those numbers which are having roots of Algebraic Equations such as the square root of 2. If √2 is a rational number then √2 = p/q where p and q are whole numbers, q is non zero. And 2 = p2/q2, or p2 = 2 * q2. From this the square of p is an even and also p itself an even number. If p is 2 times of other Whole Number then the number is p = 2x where x is this other number. Now we substitute p = 2 into the above equation 2 = p2/q2, we get,
2= (2x)2 /q2
From the above q2 is even. So that p and q both are even. That’s why √2 cannot be rational it is an irrational number. The other type is transcendental numbers and the transcendental numbers are π and e where pi is a Trigonometry function and e is Exponential Function. These are the types of Irrational Numbers. The power of irrational number can be rational. This is proved in the above algebraic numbers example of square root of two. If we again solve the above value of square root of two then the value is 2 which is a whole number.