Answer
a. $-3$
b. no real root
c. $7$
d. no real root
Work Step by Step
a. Find the real number whose cube is the radicand, $-27$:
$(-3)^{3} = -27$
Therefore, $\sqrt[3] {-27} = -3$.
b. Find the real number whose fourth power is the radicand, $-81$:
There is no real root because there is no real number whose fourth power is $-81$. The only root is imaginary.
c. Simplify the radicand first:
$\sqrt {49}$
Find the real number whose square is the radicand, $49$:
$7^{2} = 49$
Therefore, $\sqrt {49} = 7$.
d. Find the real number whose square is the radicand, $-49$:
There is no real root because there is no real number whose square is $-49$. The only root is imaginary.
