Prove that  is an irrational number.

The correct answer is: YES an irrational number.

Hint:
The real numbers which cannot be expressed in the form of p/q(where p and q are integers and q ≠ 0) are known as irrational numbers. In the given question we are asked to prove if 5-  is an irrational number. To do so we use the method of contradiction.
Solution
Let's assume that 5- is a rational number.
Step 1 of 2:
If 5- is rational, that means it can be written in the form of p/q, where p and q integers q ≠ 0.
SO 5 -  = 
5 -  = 
 = 
Step 2 of 2:
Here, we see that  is a rational number. But  is an irrational number. So our assumption is wrong.
Final Answer:
As  is an irrational number. So   must also be an irrational number. Thus, our assumption is wrong. Hence, 5- is an irrational number