Question

Given √2 is irrational prove that 3-5√2 is irrational

Answer 1

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Answer 2

Answer:

let us assume that 3-5√2 is rational

then, 3-5√2 = a/b  (where a and b are co-primes and b ≠ 0)

-5√2 = a/b - 3

-5√2 = (a-3b)/b

√2 = (a-3b)/-5b

but √2 is irrational    (given)

hence, if LHS i.e √2 is irrational , RHS is also irrational

so, our assumption is wrong

3-5√2 is IRRATIONAL

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