Prove that 11-root 3 is an irrational number

1.	Prove that 11-root 3 is an irrational number
Answer» Answer: Let us ASSUME that 11 - √3 is not an irrational 11 - √3 BECOMES rational 11 - √3 = p / q Where p , q BELONGS to integers and q ≠ 0 √3 = p / q - 11 / 1 √3 = p - 11Q / q LHS = √3 is an irrational because "3" is not a perfect square . RHS = p - 11q / q becomes rational where p , q belongs to integers and q ≠ 0 But LHS ≠ RHS It is contradiction to our Assumption . Our assumption is wrong . 11 - √3 is an irrational .

Answer»

Answer:

Let us ASSUME that

11 - √3 is not an irrational

11 - √3 BECOMES rational

11 - √3 = p / q Where p , q BELONGS to integers and q ≠ 0

√3 = p / q - 11 / 1

√3 = p - 11Q / q

LHS = √3 is an irrational because "3" is not a perfect square .

RHS = p - 11q / q becomes rational where p , q belongs to integers and q ≠ 0

But LHS ≠ RHS

It is contradiction to our Assumption .

Our assumption is wrong .

11 - √3 is an irrational .

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Prove that 11-root 3 is an irrational number ​

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Prove that 11-root 3 is an irrational number