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Question

Prove that the following is irrational : 6+2 [3 MARKS]


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Solution

Concept : 1 Mark
Application : 1 Mark
Proof : 1 Mark

Lets assume that (6+2) is rational.

It means that we have co-prime integers a and b (b0) such that ab=6+2

ab6=2

(a6b)b=2 ...(1)

a and b are integers. It means L.H.S of (1) is rational.

But we know that 2 is irrational.

L.H.SR.H.S

This contradiction arises because our assumption is wrong.

(6+2) cannot be rational.

Hence, (6+2) is irrational.


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