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Given that √2 is irrational, prove that (5+3√2) is an irrational number.

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Given that √2 is irrational, prove that (5+3√2) is an irrational number.

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1 Answer

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Let us assume (5 + 3√2 ) is a rational number

(where q ≠ 0 and p and q are integers)

⇒ √2 is a rational number as RHS is rational

This contradicts the given fact that √2 is irrational.

Hence (5 + 3√2 ) is an irrational number.

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