Question

Prove that 3 + 215 is irrational
Pro​

Answer 1

Answer:

yes

Step-by-step explanation:

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

So we can write this number as  

3 + 2√5 = a/b  

Here a and b are two co prime number and b is not equal to 0

Subtract 3 both sides we get  

2√5 = a/b 3

2√5 = (a-3b)/b

Now divide by 2 we get  

√5 = (a-3b)/2b

Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact  

Hence result is 3 + 2√5 is a irrational number