Question

prove 3+2√5 is irrational it is given that √5is irrational​

Answer 1

To prove: 3 + 2√5 is an irrational number. Proof: Let us assume that 3 + 2√5 is a rational number. This shows (a-3b)/2b is a rational number

Answer 2

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

If possible let

$3 + 2 \sqrt{5} \: \: \: is \: rational$

$\implies \: 3 + 2 \sqrt{5} - 3 \: \: is \: \: rational$

$\implies \: 2 \sqrt{5} \: \: \: is \: \: rational$

$\implies \: \frac{2 \sqrt{5} }{2} \: \: is \: \: rational$

$\implies \: \sqrt{5} \: \: \: is \: \: rational$

But this contradicts the given fact that

$\sqrt{5} \: \: \: is \: irrational$

Hence

$3 + 2 \sqrt{5} \: \: \: \: is \: \: \: irrational$

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