Question

How to prove that the square root of 3 and 5 is irrational?

Answer 1

Explanation:

• Let us assume, the contrary √3 is a rational no.
• √3 = p/q ,where p and q are co-prime
• p = √3q
• squaring on both sides
• 
  `p^(2)`/3 =
  `q^(2)`.............................(1)
• 3 is a factor of p
• p = 3c , where c is some constant
• substituting p = 3c in equation (1)
• 9
  `c^(2)` = 3
  `q^(2)`
• 
  `q^(2)`/3 =
  `c^(2)`

∴ 3 is also a factor of q

• But , this is a contradiction.
• we have assume p and q are co prime

∴ √3 is an irrational no.

• Similarly, for √5