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Question
Prove that the following are irrational.
`6+sqrt2`
Solution
`6+sqrt2`
∴ We can find two co-prime integers a and b such that `6 + sqrt2 = a/b`, Where b ≠ 0
∴ `a/b - 6 = sqrt2`
or `sqrt2 = (a/b - 6)`
= `(a - 6b)/b`
From (1), `sqrt2` is a rational number, which contradicts the fact that `sqrt2` is an irrational number.
∴ Our supposition is wrong.
= `6 sqrt2` is an irrational number.
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