Question

explain why any of the four operations (+-×÷) placed between the two terms 5 and -3√8 will result in an irrational number

Answer 1

The sum of a rational number and an irrational number is an irrational number.

Subtraction of an irrational number from a rational number is an irrational number.

Product of two irrational numbers is an irrational number.

Division of one irrational number by another irrational number is an irrational number.

From the given data, 5 is a rational number and $-3\sqrt{8}$ is an irrational number.

So, $5+(-3\sqrt{8}), 5-(-3\sqrt{8}) , 5(-3\sqrt{8}) and \frac{5}{-3\sqrt{8}}$ are all irrational numbers.