Question

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

Answer 1

Answer:

Step-by-step explanation:

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

So it can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.    

Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number  

Hence proved

Hope this helped you!