Prove that (3+5√2) is an irrational number, given that √2 is an irrational number.
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Prove that (3+5√2) is an irrational number, given that √2 is an irrational number.
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Answer:
.
Step-by-step explanation:
Let us assume the contrary.
i.e; 5 + 3√2 is rational
where ‘a’ and ‘b’ are coprime integers and b ≠ 0
That contradicts the fact that √2 is irrational.
The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.
So, 5 + 3√2 is irrational.