Simplified Radical Form with Two Terms in the Denominator

​Section 8.3
Radicals and Simplified Radical Form

Products and ​Quotients in Radical or Exponential Form

​Simplified Radical Form

Multiple Select

Select ALL expressions that are equivalent to $$\sqrt[]{75}$$ .

• $$3\sqrt[]{5}$$

• $$5\sqrt[]{3}$$

• $$75^{\frac{1}{2}}$$

• $$5\cdot3^{\frac{1}{2}}$$

• $$5^{\frac{1}{2}}\cdot3^{\frac{1}{2}}$$

Multiple Choice

Add and Simplify.

$$\sqrt[]{24}+\sqrt[]{54}$$

• $$\sqrt[]{78}$$

• $$5\sqrt[]{12}$$

• $$5\sqrt[]{6}$$

• $$6\sqrt[]{6}$$

Multiple Choice

Subtract and Simplify.

$$\sqrt[3]{40}-2\sqrt[3]{625}$$

• $$-8\sqrt[3]{5}$$

• $$-3\sqrt[3]{5}$$

• $$-8\sqrt[3]{10}$$

• $$-8\sqrt[3]{25}$$

Rationalize the Denominator with Two or More Terms

​Use the Conjugate!!

Multiple Choice

Simplify.

$$\frac{3}{1-\sqrt[]{5}}$$

• $$\frac{3+\sqrt[]{5}}{5}$$

• $$\frac{3-\sqrt[]{5}}{5}$$

• $$\frac{-3+3\sqrt[]{5}}{4}$$

• $$\frac{-3-3\sqrt[]{5}}{4}$$

Multiple Choice

Simplify.

$$\frac{\sqrt[]{3}-1}{\sqrt[]{2}-1}$$

• $$\sqrt[]{5}-\sqrt[]{2}+\sqrt[]{3}-1$$

• $$\sqrt[]{6}+\sqrt[]{3}-\sqrt[]{2}-1$$

• $$\frac{\sqrt[]{6}+\sqrt[]{3}-\sqrt[]{2}-1}{2}$$

• $$\frac{\sqrt[]{5}-\sqrt[]{2}+\sqrt[]{3}-1}{2}$$

Multiple Choice

Simplify.

$$\frac{1+\frac{1}{\sqrt[]{3}}}{1-\frac{1}{\sqrt[]{3}}}$$

• $$\frac{5+\sqrt[]{3}}{4}$$

• $$\frac{2+\sqrt[]{3}}{4}$$

• $$2+\sqrt[]{3}$$

• $$2-\sqrt[]{3}$$