Prove √2 is irrational

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Prove √2 is irrational

Posted by Satwik Dasaraddi 4 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Nitya Singh 4 years, 5 months ago

Yes

0Thank You

Yogita Ingle 4 years, 5 months ago

Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.

1Thank You

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CBSE > Class 09 > Mathematics