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Question

Prove that 2+3 is an irrational number, given that 3 is an irrational number.

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Solution

Let us assume that 2+3 is a rational number.

Thus, 2+3 can be represented in the form of pq, where p and q are integers, q ≠ 0, p and q are co-prime numbers.

2+3=pq3=pq-23=p-2qqSince, p-2qq is rational3 is rationalBut, it is given that 3 is an irrational number.Therefore, our assumption is wrong.Hence, 2+3 is an irrational number.

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