Radical Operations

Radical Operations Review

Pre-Calculus 11
McAdam

​/cube

Multiple Choice

Simplify  √48

• 4√2
• 6√3
• 4√3
• 4√2

​(or perfect cube)4n√8

Multiple Choice

Simplify the radical:  10√20

• 5√20
• 20√5
• 4√5
• 40√5

Multiple Choice

Simplify:
$$3\sqrt[3]{40}$$

• $$2\sqrt[3]{10}$$

• $$2\sqrt[3]{5}$$

• $$12\sqrt[3]{10}$$

• $$6\sqrt[3]{5}$$

Multiple Choice

SIMPLIFY:

• A
• B
• C
• D

Multiple Choice

Simplify

$$\sqrt[]{45n^3}$$

• $$3n\sqrt{5n}$$

• $$4n\sqrt{8}$$

• $$3\sqrt[]{n^3}$$

• $$5n\sqrt[]{3n}$$

Multiple Choice

• √18 + 11√2
• 22√5
• 11√20
• 14√2

Multiple Choice

$$2\sqrt{27}+8\sqrt{3}+5\sqrt{8}$$  

• $$24\sqrt{3}$$  

• $$24\sqrt{3}+5\sqrt{8}$$  

• $$14\sqrt{3}+10\sqrt{2}$$  

Multiple Choice

$$10\sqrt{45}-\sqrt{20}$$  

• $$32\sqrt{5}$$  

• $$88\sqrt{5}$$  

• $$28\sqrt{5}$$  

Multiple Choice

$$2\sqrt[3]{16x^4}+10x\sqrt[3]{54x}$$

• $$34x\sqrt[3]{2x}$$

• $$5x\sqrt[3]{2x}$$

• $$27\sqrt[3]{3}$$

• $$34x^2\sqrt[3]{2}$$

Multiple Choice

Multiply $$5\sqrt{2}\cdot4\sqrt{10}$$  

• $$20\sqrt{20}$$  

• $$10\sqrt{40}$$  

• $$40\sqrt{5}$$  

• $$9\sqrt{13}$$  

Multiple Choice

Multiply   $$\sqrt{5}\left(3-\sqrt{6}\right)$$  

• $$\sqrt{15}-\sqrt{30}$$  

• $$3\sqrt{5}-\sqrt{30}$$  

• $$-\sqrt{15}$$  

• $$\sqrt{15}-\sqrt{18}$$  

Multiple Choice

Expand $$\left(4\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}-\sqrt{3}\right)$$  

• $$20\sqrt{2}-14\sqrt{6}+2\sqrt{3}$$  

• $$46-14\sqrt{6}$$  

• $$32\sqrt{6}$$  

• $$40-14\sqrt{6}+6\sqrt{3}$$  

Multiple Choice

Expand    $$\left(10-3\sqrt{2}\right)\left(10+3\sqrt{2}\right)$$  

• $$82-\sqrt{2}$$  

• $$20-6\sqrt{2}$$  

• $$100-60\sqrt{2}$$  

• $$82$$

Multiple Choice

Find the area of the rectangle

• 11

• $$22\ +3\sqrt{6}$$

• $$22+\sqrt{42}-2\sqrt{6}$$

• $$34+11\sqrt{6}$$

​Rationalizing the Denominator

​If the denominator is monomial, multiply top and bottom by the radical

​

​​​IF the denominator is a binomial, multiply the top and bottom by the conjugate

Multiple Choice

Rationalize the denominator: $$\frac{\sqrt{5}}{2\sqrt{3}}$$  

• $$\frac{\sqrt{15}}{6}$$  

• $$\frac{\sqrt{15}}{18}$$  

• $$\frac{5\sqrt{3}}{6}$$  

• $$\frac{5\sqrt{3}}{18}$$  

Multiple Choice

Rationalize the denominator and simplify: $$\frac{7\sqrt{3}}{4\sqrt{7}}$$  

• $$\frac{7\sqrt{21}}{28}$$  

• $$\frac{7\sqrt{21}}{196}$$  

• $$\frac{\sqrt{21}}{28}$$  

• $$\frac{\sqrt{21}}{4}$$  

Multiple Choice

• A
• B
• C
• D

Multiple Choice

What is the conjugate of: $$5+\sqrt{7}$$  

• 18

• $$5+\sqrt{7}$$  

• $$5-\sqrt{7}$$  

• 32

Multiple Choice

What should you multiply $$\frac{6}{1-\sqrt{5}}$$  by to rationalize the denominator?

• -4

• $$1-\sqrt{5}$$  

• $$1+\sqrt{5}$$  

• $$-\frac{\left(3-3\sqrt{5}\right)}{2}$$  

Multiple Choice

Rationalize the following: $$\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{8}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{-2}$$  

• $$\frac{\sqrt{6}+\sqrt{10}}{8}$$  

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

Multiple Choice

$$\frac{-2}{1+\sqrt{6}}$$  Rationalize the following:

• $$\frac{1+\sqrt{6}}{-2}$$  

• $$\frac{-2+2\sqrt{6}}{-5}$$  

• $$-\frac{2\sqrt{6}}{6}$$  

• $$-2\sqrt{6}$$  

Multiple Choice

Rationalize the following: $$\frac{5+\sqrt[]{2}}{2-\sqrt[]{2}}$$

• $$14$$

• $$\frac{12+7\sqrt[]{2}}{2}$$

• $$\frac{8-3\sqrt[]{2}}{2}$$

• $$\frac{10+7\sqrt[]{2}}{4}$$