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Question

Prove the following number is irrational/not rational: 5+32


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Solution

Ir-rational number:

To prove that 5+32 is an irrational number we will use contradiction method.

Let us assume that 5+32 is a rational number, which can be represented in pq form and where q0

5+32=pq32=pq-52=p-5q3q

p-5q3q is a rational number

However, we know that 2 is an irrational number

This leads to the contradiction that 5+32 is an irrational number

Hence, the given number is an irrational number.


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