Question

To prove √2 is irrational

Answer 1

To prove √2 is irrational

STEP BY STEP EXPLANATION :::

first we should assume that √2 is rational number

√2 = a/b

b√2 = a

2b^2 = a^2 ( squaring both sides)

2 divides a^2

2divides a

a=2k

a^2=4k^2

2b^2=4k^2 ( a^2 = 2b^2 as above)

b^2 = 2k^2

2divides b^2

2 divides b

thus both a and b have a common factor 2 . It contradicts our assumption.

hence√2 is irrational.

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