Question

Prove that 3 + √5 is irrational number. ​

Answer 1

Answer:

Since rational cannot be equal to irrational no.

Therefore, our supposition is wrong that 3+√5 is a rational no. Hence it is a irrational no.

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Answer 2

Step-by-step explanation:

Let  (3 + √5) be rational.

So,      (3 + √5) = a/b            [ where a and b are co-prime and b ≠ 0]

Now,

          (3 + √5) = a/b

     =>    √5= ( a/b ) - 3

     =>    √5= ( a - 3b ) / b

Here, if (3 + √5) = a/b  is rational then, √5= ( a - 3b ) / b is also rational.

But, it contradicts the fact that √5 is irrational number.

So, our assumption was wrong.

Thus,  3 + √5 is an irrational number.              ( proved )

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