Question

Proof thar 3-√5 is irrational

Answer 1

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Your answer
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To prove : - 3 - √5 is irrational.

Proof : -

Let us assume that 3 - √5 is rational.

Then,

There must exist co-primes a and b (b ≠ 0) such that

(3 - √5) = a/b

=> - √5 = a/b - 3

=> √5 = 3 - a/b

=> √5 = (3b - a)/b

Since, a and b are integers, so (3b - a)/b is rational.

Thus, √5 is rational.

But, this contradicts the fact that √5 is irrational. So, our assumption is incorrect.

Hence, (3 - √5) is irrational.

Proved.

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