Question

show that 3√2-√5 is an irrational number​

Answer 1

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Assume 2-3√5 is a rational number

therefore 2-3√5=a/b

hence √5=a-2b/3b

therefore a-2b/3b is a rational number

therefore √5 is a rational number

but we know that √5 is a irrational number

therefore our assumption was wrong that 2-3√5 is a rational number

Therefore 2-3√5 is a irrational number..

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Hope this cleared your doubt ☺

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