Q. 4 B5.0( 1 Vote )

Prove that following numbers are irrational:


Answer :

Let be a rational number.

Therefore , where g. c. d(a, b) = 1 and a, b N.




Now, squaring both sides


……. eq (1)


15 | a2


15 | a


Now, let a = 15k, k N



So, b = 15k


15 | b



It is a contradiction as g. c. d(a, b) = 1


So, our assumption is wrong.


Therefore, is irrational.


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