Question

Prove
that 3root5-8
is an irrational number​

Answer 1

Let 3√5-8 be rational

3√5 -8 =a/b

3√5 =a/b+8

√5 = (a+8b)/3b

we know that √ 5 is irrational and (a+8b)/3b is rational therefore this is a contradiction which has arisen due to our wrong assumption that 3√5 -8 is rational.

Therefore 3√5 -8 is irrational.

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