Question

prove that 3 +√5 is irrational​

Answer 1

Explanation:

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Answer 2

ʟᴇᴛ ᴜs ᴀssᴜᴍᴇ ᴛʜᴀᴛ 3 + √5 ɪs ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

$⟹3 + \sqrt{5} = \frac{a}{b}$

• [ a, b are co - primes ]

$⟹ \sqrt{5} = \frac{a}{b} - 3 \\ \\ ⟹ \sqrt{5} = \frac{a - 3b}{b}$

↪ Here, [ (a - 3b/b) ] is a rational number .

↪ But we know that √5 is an irrational number.

↪ So, [ (a - 3b)/b) ] is also an irrational number.

↪ So, our assumption is wrong.

∴ 3 + √5 is an irrational number.

Explanation:

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