Question

Prove that the following are irrational 1/√2
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Answer 1

Answer:

Step-by-step explaination:

(i) Let 12√12 is a rational number.  12√12 = p/q √2 = q/p By Squaring on both sides,  2 × p2 = q2  2, divides q2 .  ∴ 2, divides q  ∵ q is an even number.  Similarly ‘p’ is an even number.  ∴ p and q are even numbers.  ∴ Common factor of p and q is 2.  This contradicts the fact that p and q also irrational.  

∴ √2 is an irrational number.  

∴ 12√12 is an irrational number.

Hope this helps