Question

Which choices are real numbers? Check all that apply. (-22)½ (-16)⅓ (-16)⅕ (-10)¼

Answer 1

$(-22)^{\frac{1}{2}}$ and $(-10)^{\frac{1}{4}}$ are not real numbers

Solution:

A real number is any positive or negative number. This includes all integers and all rational and irrational numbers

They are called "Real Numbers" because they are not Imaginary Numbers.

When you take an even root of a negative number, there is no real answer. (2 is an even number)

In the real number set, you can't take an even-indexed root of a negative number.

Given options are:

$\begin{array}{l}{\text { A) }(-22)^{\frac{1}{2}}} \\\\ {\text { B) }(-16)^{\frac{1}{3}}} \\\\ {\text { C) }(-16)^{\frac{1}{5}}} \\\\ {\text { D) }(-10)^{\frac{1}{4}}}\end{array}$

Looking at the answer choices here, we can see that A and D use even roots, so they will give non-real answers.

Thus $(-22)^{\frac{1}{2}}$ and $(-10)^{\frac{1}{4}}$ are not real numbers