Question

Prove that √3,2-3√5 square is irrational

Answer 1

Answer:  suppose √3 is a rational

Step-by-step explanation:

√3 = p/q , q≠0 , p & q are having common factor

             p & q re integers

squaring on both sides, we get

  (√3)²= (p/q)²

⇒ 3 =p²/q²

⇒3q²=p²

⇒q²= p²/3              (1)

⇒p² is divisible by 3

⇒then p is also divisible by 3              (2)

take p= 3r

substitute in (1), we get

⇒q²= (3r)²/3

⇒q²= 9r²/3

⇒q²= 3r²

⇒q²/3= r²

⇒q² is divisible by 3

⇒then q is also divisible by 3               (3)

from (2) and (3), we get

⇒p and q are having a common factor as 3

⇒This is a contradiction hence our supposition is false

∴ √3 is an irrational