Prove that root 2 is irrational class 10

Asked by admin @ 25/08/2021 in Math viewed by 289 People

Prove that √2 is irrational.
Class 10 - cbse

Answered by admin @ 25/08/2021

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.

hope this helps

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Prove that root 2 is irrational class 10

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