Question

show that 3root is an irrational numbet​

Answer 1

let √3 be rational number.

√3 = p/q

Squaring both sides

(√3)² = (p/q)²

3 = p²/q²

3q² = p²

here,

3 divide p

and

3 also divides p²......(¡)

let p be 3

3q ² =(3)²

3q² = 9

q² = 3.....(¡¡)

3 divide q

and

3 also divide q²

from (¡) and (¡¡) we get,

3 is a common factor of p and q.

so, our assumption is wrong

√3 is an irrational number.

here is your answer...