Question

3+2√5
prove that irrational​

Answer 1

Step-by-step explanation:

here we can say 3+2√5 is an irrational.

Answer 2

Answer:

I think it helps you ⬇️⬇️

Step-by-step explanation:

We will prove this by contradiction.

Let us suppose that 3+2√5 is rational.

It means that we have co-primes Integers 'a' and 'b'

(b is not equal to 0) such that,

$\frac{a}{b} = 3 + 2 \sqrt{5}$

$\frac{a}{b} - 3 = 2 \sqrt{5}$

$\frac{a - 3b}{b} = 2 \sqrt{5}$

$\frac{a - 3b}{2b} = \sqrt{5}$

'a' and 'b' are Integers.

It means L.H.S is rational, but we know that √5 is irrational.It is not possible.

Therefore,our assumption is wrong,3+2√5 cannot be rational.

Hence 3+2√5 is irrational

Please mark it as brainlist answer ✍️✍️