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Question

Prove that 3+25 is irrational. [4 MARKS]


Solution

Concept : 1 Mark
Application : 1 Mark
procedure : 2 Marks

Let us assume, to the contrary, that 3+25 is rational.

That is, we can find co-prime integers a and b(b0) such that 3+25=ab

Therefore, ab3=25

a3bb=25

a3b2b=5

a2b32=5

Since a and b are integers, we get a2b32 is rational, and so a3b2b=5 is rational.

But this contradicts the fact that 5 is irrational.

L.H.SR.H.S

This contradiction has arisen because of our incorrect assumption that 3+25 is rational.

So, we conclude that 3+25 is irrational.


Mathematics

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