Question

prove the root 3 is irrationl number​

Answer 1

your answer is given in picture.......

Answer 2

Answer:

Step-by-step explanation:

let us assume that √3 is a rational number

⇒√3=p/q (where p,q∈positive integers,q≠0 and H.C.F (p,q)=1)

squaring on both sides

⇒3=p²/q²

⇒p²=3q²→equation 1

⇒3 divides p² then 3 divides p

by using euclid algorithm

⇒p=3k

in equation 1

⇒(3k)²=3q²

⇒9k²=3q²

⇒q²=3k²

here 3 divides q² then 3 divides q

∴p,q have common factor 3→equation 2

but p,q have common factor 1

∴this is our contradiction that √3 is a rational number is wrong

∴√3 is an irrational number

hope you understand