Is the number ​𝜋+–

Question

5 rational or irrational?

Answer 1

The expression \(\pi \pm 5\) involves the number \(\pi\), which is known to be irrational.

A rational number can be expressed as the fraction of two integers (i.e., of the form \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\)). An irrational number cannot be expressed in this way.

When you add or subtract a rational number (in this case, 5, which is rational) from an irrational number (like \(\pi\)), the result is still irrational.

Therefore, both \(\pi + 5\) and \(\pi - 5\) are irrational numbers. So, the answer is that \(\pi \pm 5\) is irrational.