9. Roots, Radicals, and Complex Numbers

Use the product rule to multiply the following.

$\sqrt{8}\cdot \sqrt[3]{2}$

Use the quotient rule to simplify.

$\sqrt{\frac{x^2}{36}}$

Use the quotient rule to divide, then simplify.

$\frac{\sqrt{144}}{\sqrt{16}}$

Use the quotient rule to divide, then simplify.

$\frac{\sqrt{75}}{\sqrt{3}}$

Simplify the following.

$\sqrt{\frac{9}{x^2}}$

Use the product rule to multiply the following.

$\sqrt{5x}\cdot \sqrt{7y}$

Use the quotient rule to simplify.

$\sqrt{\frac{2}{81}}$

Simplify the following.

${}^4\sqrt{256a^8{b}^9}$

Use the product rule to rewrite the term inside the radical as a product, then simplify.

$\sqrt{180}$

Simplify the following.

$\sqrt{\frac{100a^6{b}^2}{25x^2}}$

Simplify the following.

${}^4\sqrt{80y^5}$

Use the product rule to rewrite the term inside the radical as a product, then simplify.

$-\sqrt{72x^2}$

Use the product rule to multiply the following.

$\sqrt[4]{7m^2}\cdot \sqrt[4]{2n}$

Simplify the following.

$\sqrt{49m^2}$

Use the product rule to multiply the following.

$\sqrt{6}\cdot \sqrt{5}$