Question

Can you name a real number that is represented by the square root of negative 36

Answer 1

Let's start by knowing what a real number is. A real number is a quantity that can be plotted in a number line or a Cartesian plane. So all integers, rational numbers and radical numbers are real numbers. The only instance when it is not real, is when they are imaginary. These are still numbers, but they have a term 'i' associated with them. Numerically, i = √-1. There is no equivalent quantity to a root of any negative number. It can't be placed anywhere in the number line.

So, for the problem where the number is √-36, we can simplify that to

√-36 = √-1(36) = 6√-1 = 6i

Hence, √-36 is equal to 6i. It can't be expressed into a real number in any way.

However, I'm going to add an additional information. An imaginary number could become real when raised to the power of 2 or 4. This is because

i = √-1
i² = -1
i⁴ = 1

In that case, the number becomes real.