Prove that root 3 is irrational and hence prove that root 3+ root 5 is irrational

2 thoughts on “Prove that root 3 is irrational and hence prove that root 3+ root 5 is irrational”

1. Let as assume on contrary that

   √3 + √5

   is a rational number.

   Then there exists co – prime integers p and q such that

   ⇒ √3

   is a rational number .

   But this contradicts the fact that

   √3

   is irrational.

   So, our assumption is wrong.

   Hence,

   √3 + √5

   is irrational.

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2. Answer:

   Let √3+√5 be a rational number. A rational number can be written in the form of p/q where p,q are integers. … But this contradicts the fact that √5 is an irrational number. So,our supposition is false.

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