Question

EX
Prove that 15 is irrational
Prove that 3 + 215 is irrational​

Answer 1

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