Question

Prove that 3+2√5is an irrational number​

Answer 1

Answer:

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

So we can write this number as  

3 + 2root5 = a/b  

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

Subtract 3 both sides we get  

2root5 = a/b � 3

2root5 = (a-3b)/b

Now divide by 2 we get  

root5 = (a-3b)/2b

Here a and b are integer so (a-3b)/2b is a rational number so root5 should be a rational number But root5 is a irrational number so it contradict the fact  

Hence result is 3 + 2root5 is a irrational number

Step-by-step explanation: