Answer
a) $5^{\frac{1}{3}}$
b) $\sqrt 5$
c) See explanation
Work Step by Step
a)$\sqrt[3] 5$ = $\sqrt[3]( 5^{1})$= $5^{\frac{1}{3}}$
b) $5^{\frac{1}{2}}$ = $\sqrt[2]( 5^{1})$ = $\sqrt 5$
c) They are numerically equal, but they involve different operations:
- in $\sqrt{5^2}$, you square first, then take a square root.
- in $(\sqrt 5)^2$, you take the square root first, then square.
