Q. 4 A3.7( 6 Votes )

Prove that following numbers are not rational :

(6)1/3

Answer :

Suppose 61/3 is rational.

Then, 61/3 = for some integers n and m which are co-prime.


So, 6 =


6m3 = n3


So, n3 must be divisible by 6


n must be divisible by 6.


Let n = 6p for some integer p


This gives


6 =


1 =


m3 is divisible by 6


Hence, m must be divisible by 6.


But n and m where co-prime.


So, we have a contradiction.


Hence, (6)1/3 is irrational


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