Class 10 -Prove √3 is a Irrational number.
Prove √3 is a Irrational number . Proof: Let √3 be a rational number. So, √ 3 = p ____ (1) q On squaring both sides 3 = p 2 q 2 q 2 = p 2 3 ⇒ 3 is a factor of p 2 ⇒ 3 is a factor of p. Now, again let p = 3 c. So, √ 3 = 3 c q On squaring both sides 3 = 9 c 2 q 2 q 2 = 3 c 2 c 2 = q 2 3 ⇒ 3 is factor of q 2 ⇒ 3 is a factor of q. Here 3 is a common factor of p, q both So p, q are not co-prime. Therefore our assumption is wrong. √ 3 is an irrational number.