Simplify by first writing in radical form.

$$-27^{5 / 3}$$

Determine this product. To ensure that the answers are simple, refer to the five criteria provided in this section.

$$(5-\sqrt{2})(5+\sqrt{2})$$

Rationalize this denominator. Write $\frac{2+\sqrt{8}}{4}$ in lowest terms.

Determine this square root.

$$-\sqrt{256}$$

Rationalize this denominator.

$$\sqrt{\dfrac{1}{32}}$$

Simplify by first writing in radical form.

$$-8^{2 / 3}$$

Simplify this radical expression. $\sqrt{5}$ \cdot $\sqrt{15}$

Simplify this radical.

$$\sqrt{75}$$

Solve this equation.

$$k=\sqrt{k^2-5 k-15}$$

Perform this indicated operations, and express each response in its most basic form. Assume  the variable being positive real number.

$$\sqrt[3]{\dfrac{16}{81}}$$

Determine this product. To ensure that the answers are simple, refer to the five criteria provided in this section.

$$(\sqrt{7}+2)^2$$

Simplify by first writing in radical form.

$$144^{3 / 2}$$

Perform this indicated operations, and express each response in its most basic form. Assume  the variable being positive real number.

$$(5+3 \sqrt{3})^2$$

Find whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. Give a decimal approximation rounded to the next thousandth if a value is irrational. Calculators should be used when needed.

$$\sqrt{-4}$$