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Prove that root 2 a irrational …

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Prove that root 2 a irrational number

Posted by Arjun Mishra 7 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 7 years, 5 months ago

Given √2 is irrational number.
Let √2 = a / b wher a,b are integers b ≠ 0
we also suppose that a / b is written in the simplest form
Now √2 = a / b
⇒ 2 = a² / b²
⇒ 2b² = a²
∴ 2b² is divisible by 2
⇒ a² is divisible by 2
⇒ a is divisible by 2
∴ let a = 2c
a² = 4c²
⇒ 2b² = 4c²
⇒ b² = 2c²
∴ 2c² is divisible by 2
∴ b² is divisible by 2
∴ b is divisible by 2
∴ a are b are divisible by 2 .
This contradicts our supposition that a/b is written in the simplest form
Hence our supposition is wrong
∴ √2 is irrational number.

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CBSE > Class 09 > Mathematics