# Prove that 3+ √5 is an irrational number.

Irrational numbers are those real numbers that cannot be represented in the form of a/b.

## Answer: 3+ √5 is an irrational number

Let us see, how to solve.

**Explanation**:

Let us assume that 3 + √5 is a rational number.

Now,

3 + √5 = a/b

[Here a and b are co-prime numbers, where b ≠ 0]

√5 = a/b - 3

√5 = (a - 3b)/b

Here, {(a - 3b)/b} is a rational number.

But we know that √5 is an irrational number.

So, {(a - 3b)/b} should also be an irrational number.

Hence, it is a contradiction to our assumption.

Thus, 3 + √5 is an irrational number.

### Hence proved, 3 + √5 is an irrational number.

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