Question

prove that square root of 3 is irrational
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Answer 1

Step-by-step explanation:

i think it is long but it will help you

Answer 2

Answer:

Step-by-Let √3 be a rational number  

i.e. √3 = a/b where a,b ∈ integers having no common factor other then 1 and b≠0

= √3 = a/b

square both the sides

= 3= a²/b2

= a² = 3b²

= b² = a²/3

= 3 divides a²

= 3 divides a²

let a²= 3c

= b²=9c²/3

= b²= 3c²

= c²= b²/3

= 3 divides b²

= 3 divides b

thus 3 is a common factor of a and b

this contradicts the fact that a and b are coprime numbers i.e. having no common factor other then 1.

therefore √3 is not a rational number  

hence it is irrational

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step explanation: