Answer :

**Given:** Any prime positive integer p.

**To find:** is an irrational number.

**Concept used:** Assume p to be rational number and prove it is irrational by contradiction.

**Explanation:**

_{Let assume that √p is rational}

_{Therefore, it can be expressed in the form of} , where a and b are integers and b≠0

Therefore, we can write

a^{2} = pb^{2}

Since a^{2}is divided by b^{2}, therefore a is divisible by b.

Let a = kc

(kc)^{2}= pb^{2}

K^{2}c^{2}= pb^{2}

Here also b is divided by c, therefore b^{2} is divisible by c^{2}. This contradicts that a and b are co-primes. Hence is an irrational number.

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