Question

prove that 3+2√5 is irrational
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Answer 1

Answer:

$3 + 2 \sqrt{5}$

see that and try to understand

it's f

√5 is not divisible

and if you add 3and 2 then 5 so its 5√5 it's impossible to formed in p/q

Step-by-step explanation:

so it's irrational

Answer 2

Answer and Step-by-step explanation:

Prove that 3+2√5 is irrational

Given:3 + 2√5

To prove:3 + 2√5 is an irrational number.

Proof:

Let us assume that 3 + 2√5 is a rational number.

So it can be written in the form a/b

3 + 2√5 = a/b

Here a and b are co-prime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

so it contradict sour assumption.

Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved .