Question

Prove that 3+2root5 is an irrational number?

Answer 1

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Answer 2

Hi there!

Suppose 3 + 2√5is rational .

Let 3 + √2 = r       [ where r is a rational. ]

∴  (3 + 2√5)² = r²

∴  29 + 12√5 = r²

∴ √5 = r²-29 / 12

Now , LHS = √5 is an irrational number .

RHS =  (r²-29 ) / 12,  But rational number cannot be equal to an irrational.

∴ Our supposition is wrong.

∴ 3 + 2√5 is irrational .

[ Thank you! for asking the question. ]
Hope it helps!