Maths-

General

Easy

Question

# 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

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