Question

prove that root 2 is a irrational number ​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

LET √2 BE A RATIONAL NUMBER

SO √2 = p/q where q is not = 0 and p and q are co prime

on cross multiplying we get

=√2q = p

on squaring both side we get

= 2q^2 = p^2 -------(1)

so p^2 is divisible by 2 then p is also divisible by 2

LET C BE OTHER FACTOR SO ,

= 2p = C

ON SQUARING BOTH SIDE WE GET ,

= 4p^2 = C^2

= p^2 = c^2/2 ----(2)

PUT VALUE FROM EQUATION (2) IN (1)

=2q^2 = c^2/2

ON CROSS MULTIPLYING WE GET ,

= 4q^2 = c^2

so c^2 is divisible by 4 so C is also divisible by 4

but this contradict the statement that p and q are co prime

this contradiction has arisen due to our wrong assumption that √2 is rational

so we contradict that √2 is irrational

_____________HENCE PROVED___________