Answer
(a) Answer is $>$
(b) Answer is $>$
Work Step by Step
(a) The answer can be deduced logically, since $3^{\frac{1}{2}}$ is $\sqrt{3}$ and $3^{\frac{1}{3}}$ is $\sqrt[3] 3$. A square root breaks the number into 2 factors, while the cubic root breaks the number into 3 factors; therefore, the square root must be larger.
(b) The answer can be estimated by the using numbers with perfect squares as a guide:
$$4 < 7 < 9$$
Therefore,
$$\sqrt{4} < \sqrt{7} < \sqrt{9}$$$$= 2 \sqrt{7 + 18}$$
