Question

prove that 3+2√5 is irrational



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Answer 1

Answer:

⭐

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

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

Answer 2

Answer:

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