Question

Prove that root 3 + root 5 is an irrational number.

Answer 1

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. p,q are integers then (p²+2q²)/2pq is a rational number. Then √5 is also a rational number

Step-by-step explanation:

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Answer 2

Answer:

let x be a rational number equal to 3+ root 5

3+ root 5= x

squaring both sides

(3+ root 5)(3+ root 5)= x square

14+6 root 5= x

6 root 5= x-14

as we know that x is a rational number, RHS is rational but since 6 root 5 is irrational therefore, LHS is irrational.

LHS is not equal to RHS

therefore, 3 + root 5 is irrational