Question

Prove that 3+3√5 is irrational .

Answer 1

$3 + 3 \sqrt{5} \\ 6 \sqrt{5}$

in simple language any number having a square root is irrational

Answer 2

To prove:

• 3+3√5 is an irrational no

Proof:

The proof below is based on assumption and contradiction.

Let us assume on an contrary that 3 + 3√5 is rational.

Then,

⇒ 3 + 3√5 = p/q

Where p, q are integers and q is not equals to 0.

⇒ 3√5 = p/q - 3

⇒ 3√5 = p - 3q / 3

⇒ √5 = p - 3q / 9

Since p, q, 3 and 9 are rational numbers, p - 3q / 9 is also a rational number.

But this contradicts the fact that √5 is an irrational number. This contradiction has arisen due to our wrong assumption that 3 + 3√5 is a rational number.

Thus,

3 + 3√5 is a irrational number. Hence, proved!!!