Question

prove that 3+√5 is an irrational number. please answer my question
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Answer 1

Answer:

let us assume that 3+√5 is an rational number

3+√5=p/q

√5=p-3q/q

here p-3q/q is a ratoinal number but√5 is an irrational number

=our assumption is wrong

3+√5 is an irrational number

Answer 2

Answer:

Let us assume that 3 + root 5 is rational.

Step-by-step explanation:

There exists coprime integer p and q where q is not equal to zero.

Therefore 3 + root 5 = p/q

Root 5 = p/q -3

Root 5 = p- 3q/q

Root 5 is rational and p- 3q/q is rational (as assumed).

But rational number cannot be equal to an irrational number.

Therefore 3 + root 5 is an irrational number .

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