Question

3+2√5 is irrational prove that​

Answer 1

Answer:

answer √5 is irrational number but a/2b- 3b is rational

Step-by-step explanation:

1. let us assume that 3+2 √5 is irrational number
2. 3+2√5 ( where and b are the integers
3. 2√5=a\b-3
4. 2√ 5 =a/ b - 3b
5. √5= a/2b-3b
6. hence √5 is irrational number but a/ 2b- 3b is rational number
7. our assumption is wrong √5 is irrational but a/2b-3b is rational

Answer 2

Answer:

Let 3+ 2√5 be rational number.

We know that rational number is in the p/q form , where p and q are integer .

p/ q = 3 +2√5

p/q -3 = 2√5

p -3q/q = 2√5

p- 3q /2q = √5

:.p-3q/2q is in p/q form so, it is rational

number but we know that √ 5 is an irrational number.

:. My contradiction is wrong.

Hence, 3+2√5 is an irrational number.