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Question
Prove that of the numbers `3/sqrt(5)` is irrational:
Solution
Let `3/sqrt(5)` be rational.
∴ +`1/3 × 3/sqrt(5) = 1/sqrt(5)` = rational [∵Product of two rational is rational]
This contradicts the fact that `1/sqrt(5)` is irrational.
∴` (1 × sqrt(5))/(sqrt(5) × sqrt(5)` = `1/5 sqrt(5)`
So, if `1/sqrt(5)` is irrational, then `1/5 sqrt(5)` is rational
`∴ 5 xx 1/5 sqrt(5) = sqrt(5)=` ration [ ∴ Product of two rationalis rational ]
Hence `1/sqrt(5)` is irratonal
The contradiction arises by assuming `3/sqrt(5)` is rational.
Hence, `3/sqrt(5)` is irrational.
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