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

Answer:
`(-16)^{(1)/(5)}` And
`(-4)^{(1)/(3)}`

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)^{(1)/(5)}`

Negative number is not inside the square root.

⇒ It is a real number.

In expression
`(-10)^{(1)/(4)}=((-10)^{(1)/(2)})^{(1)/(2)}`

Negative number is inside the square root.

⇒ It is a non real number

In expression
`(-4)^{(1)/(3)}`

Negative number is not inside the square root.

⇒ It is a real number

In expression
`-32^{(1)/(3)}=((-32)^{(1)/(3)})^{(1)/(2)}`

Negative number is inside the square root.

⇒ It is a not real number.

Answer 2

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!