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Prove that 3+2√5 is irrationaldelete My Question​

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ANSWER:

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Step-by-step explanation:

Prove 3 + 2 \sqrt{5} is IRRATIONAL

⇾let \: take \: 3 + 2 \sqrt{5} \: is \: rational \: number \\

⇾so, we can write this answer

⟹3 + 2 \sqrt{5} = \frac{a}{b} \\

Here a & b use TWO comprise number and b ≠ 0

\sf\mathbb\color{red} {⟹2 \sqrt{5} = \frac{a}{b} - 3}

\sf\mathbb\color{red} {⟹2 \sqrt{5} = \frac{a - 3b}{b} }

\sf\mathbb\color{red} {∴ \: \: \: \sqrt{5} = \frac{a - 3b}{2b} }

Here a and b integers so \frac{a - 3b}{2b} Is a Rational number so \sqrt{5} Should be rational number but \sqrt{5} is a irrational number so it is contradict

- hence \: 3 + 2 \sqrt{5} \: is \: irrational \:


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