Question

prove that √2 is not a rational number​

Answer 1

Step-by-step explanation:

let √2 represent a rational numbers

and √2 can be expressed in the form of p/q, where p, q are integer, q is not equal to 0

√2 = p/q

squaring both sides , we get

2 =p²/q²

p²= 2q²........................(1)

2 divides p²

2 divides p................... (2)

let p = 2m

p²= 4m²

putting the value of p² in (1) , we get

4m² = 2q²

2 m² = q²

2 divides q...................... (3)

thus from (2) , 2 divides p and from (3) , 2 also divides q

it means 2 is a common factors of production and q

this contradicts the supposition so there is no common factor of p and q

Hence √2 is an irrational number