Question

please solve this question is urgently please​

Answer 1

Refer above attachment

Answer 2

Answer:

let us assume that √3 is irrational

√3=p/q where we p, q€z, q≠0is ,P, q are co primes

squaring on both sides

3=p^2

3q^2=p^2

• hence 3 is a factor of p^2}[p is prime, If p divides a^2then p divides a](1)
• also 3 is a factor of p (1)

let p=3m

3q^2=(3m)^2

3q^2=9m^2

q^2=3m^2

• hence 3 is a factor of q^2{p is prime, If p divides a^2 then p divides a }(2)
• also 3 is a factor of q (2)

from 1 and 2

3 is a common factor for both p and q but p, q which is a contradiction

This is because of our wrong assumption

√3 is irrational

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