Question

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

Answer 1

Answer:

Step-by-step 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