Q. 4 A3.7( 6 Votes )

# Prove that following numbers are not rational :(6)1/3

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.

Hence, (6)1/3 is irrational

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