Question

Which choices are real numbers? Check all that apply.
a. (-16)^1/5
b. (-10)^1/4
c. (-4)^1/3
d. (-32)^1/6

Answer 1

Real numbers can't take the square root of a neg ative number.

Therefore the answers are:

a. (-16)^1/5

c. (-4)^1/3

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

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

Answer: $(-16)^{\frac{1}{5}}$ And $(-4)^{\frac{1}{3}}$

Step-by-step explanation:

If there is a negative number inside a square root or if a negative number has power 1/2 then it is called a non real number or complex number.

In expression $(-16)^{\frac{1}{5}}$  

Negative number is not inside the square root.

⇒ It is a real number.

In expression $(-10)^{\frac{1}{4}}=((-10)^{\frac{1}{2}})^{\frac{1}{2}}$  

Negative number is inside the square root.

⇒ It is a non real number

In expression $(-4)^{\frac{1}{3}}$  

Negative number is not inside the square root.

⇒ It is a real number

In expression $-32^{\frac{1}{3}}=((-32)^{\frac{1}{3}})^{\frac{1}{2}}$  

Negative number is inside the square root.

⇒ It is a not real number.