Question

Prove Ö5 is irrational 3+2Ö5 is irrational number.

Answer 1

Step-by-step explanation:

Let us assume 3+2

5

+ is rational.

So we can write this number as

3+2

5

=

b

a

---- (1)

Here a and b are two co-prime number and b is not equal to zero.

Simplify the equation (1) subtract 3 both sides, we get

2

5

=

b

a

−3

2

5

=

b

a−3b

Now divide by 2 we get

5

=

2b

a−3b

Here a and b are integer so

2b

a−3b

is a rational number, so

5

should be a rational number.

But

5

is a irrational number, so it is contradict.

Therefore, 3+2

5

is irrational number