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Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

$\sqrt{\frac{75{r}^{6}{s}^{8}}{48r{s}^{4}}}$

Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

$\sqrt{\frac{27{p}^{2}q}{108{p}^{5}{q}^{3}}}$

Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

$\sqrt{\frac{50{r}^{5}{s}^{2}}{128{r}^{2}{s}^{5}}}$

• ⓐ Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify $\sqrt{288}$ to determine the length and the width of his garden. Round to the nearest tenth of a foot.
• ⓑ Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify $\sqrt{288}-5$ to determine the length and width of the new garden. Round to the nearest tenth of a foot.

• ⓐ Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground. Simplify $\sqrt{\frac{64}{16}}$ to determine the number of seconds it takes for the sunglasses to reach the ground.
• ⓑ Suppose the sunglasses in the previous example were dropped from a height of 144 feet. Simplify $\sqrt{\frac{144}{16}}$ to determine the number of seconds it takes for the sunglasses to reach the ground.

Explain why $\sqrt{{x}^{4}}={x}^{2}$. Then explain why $\sqrt{{x}^{16}}={x}^{8}$.

Explain why $7+\sqrt{9}$ is not equal to $\sqrt{7+9}$.

Add: ⓐ $3x+9x$ ⓑ $5m+5n$.

Simplify: $\sqrt{50{x}^{3}}$.

Simplify: $2\sqrt{2}-7\sqrt{2}$.

Simplify: $8\sqrt{2}-9\sqrt{2}$.

Simplify: $5\sqrt{3}-9\sqrt{3}$.

Simplify: $3\sqrt{y}+4\sqrt{y}$.

Simplify: $2\sqrt{x}+7\sqrt{x}$.

Simplify: $5\sqrt{u}+3\sqrt{u}$.

Simplify: $4\sqrt{x}-2\sqrt{y}$.

Simplify: $7\sqrt{p}-6\sqrt{q}$.

Simplify: $6\sqrt{a}-3\sqrt{b}$.

Simplify: $5\sqrt{13}+4\sqrt{13}+2\sqrt{13}$.

Simplify: $4\sqrt{11}+2\sqrt{11}+3\sqrt{11}$.