Question

WILL FAN AND MEDAL

Which choices are real numbers? pick all that apply.

A (-256)^1/9
B (-131072)^1/16
C(-1024)^1/4
D (-531441)^1/13

Answer 1

what do you know about real numbers..?

Answer 2

here is a link to a nice maths dictionary with a definition and examples of real numbers

Answer 3

@Michele_Laino

Answer 4

A= irrational #, reall numbers

Answer 5

oops here is the link

http://www.mathsisfun.com/numbers/real-numbers.html

Answer 6

I think only A. and D. because even if they are negative the denominator of their exponent is odd, namely 9, and 13 respectively, so there aren't any problem with the sign of the radicand.
For example B. is a complex number, because we can write:
\[\sqrt[16]{-131072}=\sqrt[16]{2^{16}*(-2)}=2*\sqrt[8]{\sqrt{-2}}\]
which is not a real number

Answer 7

C is not a real number, please note that:
\[\sqrt[4]{-1024}=\sqrt[4]{-2^{10}}=\sqrt{-2^{5}}=2^{2}\sqrt{-2}\]
which is a complex number
@Dianie

Answer 8

more explanation:
for example:
case A:
\[\sqrt[9]{-256}=\sqrt[9]{-1*256}=\sqrt[9]{-1}*\sqrt[9]{256}=-1*\sqrt[9]{256}\]
and you can see that is a real number

Answer 9

case D. goes the same, please note that:
\[\sqrt[13]{-531441}=\sqrt[13]{-1}*\sqrt[13]{531441}=-1*\sqrt[13]{531441}\]