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InterviewSolution
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Prove that ` (3 + 5sqrt2)` is irrational. |
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Answer» Let us assume, to the contrary , that ` (3 + 5sqrt2)` is rational. Then , there exist co-primes a and b ` ( b ne0)` such that ` 3 +5sqrt2= a/b` ` Rightarrow 5sqrt2 = a/b -3 = (a -3b)/b` ` Rightarrow sqrt2 = (a-3b)/(5b)` is rational. Thus, `sqrt2` is also rational. But, this contradicts the fact that ` sqrt2` is irrational. So, our asumption is incorrect. Hence, ` ( 3+5sqrt2)` is irrational. |
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