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Prove that root 3 irrational.

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Prove that root 3 irrational.

Posted by Animesh Kumar 7 years, 3 months ago

CBSE > Class 10 > Mathematics

3 answers

Swati Khatri 7 years, 3 months ago

Let root 3 is a rational no. Therefore root 3 = P/q (where q# 0) Squaring both side 3 =p^2/ q^2 3q^2 = p^2 Because p^2 divided by 3 Therefore P also divided by 3 Now, P = 3m Squaring both side (p)^2 = (3m)^2 3q^2 = 9m^2 q^2 =9/3 =3 q^2= 3m^2 Because q^2 divided by 3 Therefore q also divided by 3 Therefore p and q have at least 3 as a common factor. So our assumption root 3 is a rational no. is incorrect.

Krishna Priya Vijayan 7 years, 3 months ago

We have assume √3 is rational Therefore √3 =p/q and p and q are co primes p not equal to 0 Therefore p = √3q Squaring on both sides p^2 = 3q^2 Theorem : let p be a prime number ,it divides a^2 than p divides a, where a is a positive integer 3 divides q ^2 . 3 divides q Let p = 3x (3x)^2 =3q ^2 9x^2 = 3 q ^2 3x^2 = q ^2 Theorem : let p be a prime number ,it p divides a^2 than p divides a where a is a positive integer 3 divides q^2 3 divides q That mean p and q has 2 common factor Which is a contradicts the fact a and b Therefore √3 is irrational

Gur Maan 7 years, 3 months ago

Root 3 is a rational number Where a and b are positive integer and has on common number (Root 3) =a÷b 3a=b 3 divodes a Put a= 3m in eq 1 3.b2 =9m b2= 3m 3divides b So root3 has common number Which is contradication So root3 is an irrational number

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