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Prove that √3 is an irrational number. Hence, show that 7 + 2√3 is also an irrational number.

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Prove that √3 is an irrational number. Hence, show that 7 + 2√3  is also an irrational number.

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If possible, let √5 be a rational number

q ≠ 0 and p and q are co-Primes

p - 7 q and 2 q both are integers, hence √3 is a rational number.

But this contradicts the fact that √3 is an irrational

number. Hence 7 + 2√3 is irrational.

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