Algebra 2 6-2 Guided Practice: Multiplying and Dividing Radical Expressions

Last updated about 3 years ago

25 questions

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8

5

A.SSE.2

5

3

10

9

3

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3

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A.SSE.2

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A.SSE.2

Library

Algebra 2 6-2 Guided Practice: Multiplying and Dividing Radical Expressions

Last updated about 3 years ago

25 questions

3

10

A.SSE.2

Take Note: Take a moment to record the property Combining Radical Expressions: Products in your notes.

3

8

Draggable item		Corresponding Item

5

A.SSE.2

5

3

10

9

10

A.SSE.2

3

8

Draggable item		Corresponding Item

10

A.SSE.2

Take Note: Take a moment to record the property Combining Radical Expressions: Quotients in your notes.

3

8

Draggable item		Corresponding Item

10

Problem 4 Got It? What is the simplest form of the expression?

A.SSE.2

3

10

Take Note: What is meant by rationalizing a denominator ?

10

Problem 5 Got It? What is the simplest form of the expression?
Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

A.SSE.2

10

A.SSE.2

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Take a moment to record the property Combining Radical Expressions: Products in your notes.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

Draggable item		Corresponding Item
2^{2}\cdot 5^{2}		(2\cdot 5)^3
\sqrt{2\cdot 5}		(2\cdot 5)^2
2^{3}\cdot 5^{3}		\sqrt[3]{2}\cdot \sqrt[3]{5}
\sqrt[3]{2\cdot 5}		\sqrt{2}\cdot \sqrt{5}

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not.

No; The indexes are different.

Yes;

Yes; 

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not.

Yes; 

No; The indexes are different.

Yes; 

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Recall that it is valuable to recognize perfect squares when simplifying square root expressions. Classify each number on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

144
25
3
7
1
4
21
200
2
9

Perfect square
NOT perfect square

Take Note: Recall that it is valuable to recognize perfect cubes when simplifying cube root expressions. Classify each number on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

125
-8
3
4
9
-64
1
-16
27
1000

Perfect cube
NOT perfect cube

Take Note: Classify each radical expression on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

\sqrt{3ab}
-2\sqrt{3}
4\sqrt{200}
2\sqrt{6}
\sqrt{24}
-3x\sqrt{5x^{2}}
\sqrt{t^{5}}
\sqrt{12}
16b^{5}\sqrt{7b}

In simplest form
NOT in simplest form

10

A.SSE.2

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Match each radical expression on the left with its simplest form on the right.

Draggable item		Corresponding Item
\sqrt[3]{8x}\cdot \sqrt[3]{3x}		2x\sqrt{3}
3\sqrt{x^{3}}\cdot \sqrt{8y}		2\sqrt[3]{3x^{2}}
\sqrt{xy^{2}}\cdot \sqrt{36}		6x\sqrt{2xy}
2\sqrt{3x^{2}}		6y\sqrt{x}

10

A.SSE.2

Take Note: Take a moment to record the property Combining Radical Expressions: Quotients in your notes.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

Draggable item		Corresponding Item
\frac{\sqrt[3]{3}}{\sqrt[3]{7}}		\sqrt{3\cdot 7}
\sqrt[3]{3\cdot 7}		\frac{\sqrt{3}}{\sqrt{7}}
\sqrt{3}\cdot \sqrt{7}		\sqrt[3]{3}\cdot \sqrt[3]{7}
\sqrt{\frac{3}{7}}		\sqrt[3]{\frac{3}{7}}

Problem 4 Got It? What is the simplest form of the expression?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Take Note: What is meant by rationalizing a denominator ?

10

Take Note: Provide an example of a rational expression that includes an irrational denominator.

10

Take Note: Provide an example of a rational expression that includes a rationalized denominator.

Problem 5 Got It? What is the simplest form of the expression?
Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

10

A.SSE.2

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Solve It! You can cut the 36-square into four 9-squares or nine 4-squares. Which other n-square can you cut into sets of smaller squares in two ways?

A 64-square

A 49-square

An 18-square

Solve It! Is there a square you can cut into smaller squares in three ways? Explain.

Yes, any n-square where n is the product of three perfect squares can be cut into smaller squares in three ways.

No, this only works when n is a perfect square and only creates two ways in which to divied the n-square into squares.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

2^{2}\cdot 5^{2}

(2\cdot 5)^3

\sqrt{2\cdot 5}

(2\cdot 5)^2

2^{3}\cdot 5^{3}

\sqrt[3]{2}\cdot \sqrt[3]{5}

\sqrt[3]{2\cdot 5}

\sqrt{2}\cdot \sqrt{5}

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not. 

No; The indexes are different.

Yes;

Yes; 

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not. 

Yes; 

No; The indexes are different.

Yes; 

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Recall that it is valuable to recognize perfect squares when simplifying square root expressions. Classify each number on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it. 

Perfect square

NOT perfect square

Take Note: Recall that it is valuable to recognize perfect cubes when simplifying cube root expressions. Classify each number on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it. 

125

-8

3

4

9

-64

1

-16

27

1000

Perfect cube

NOT perfect cube

Take Note: Classify each radical expression on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it. 

\sqrt{3ab}

-2\sqrt{3}

4\sqrt{200}

2\sqrt{6}

\sqrt{24}

-3x\sqrt{5x^{2}}

\sqrt{t^{5}}

\sqrt{12}

16b^{5}\sqrt{7b}

In simplest form

NOT in simplest form

Problem 2 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Match each radical expression on the left with its simplest form on the right.

\sqrt[3]{8x}\cdot \sqrt[3]{3x}

2x\sqrt{3}

3\sqrt{x^{3}}\cdot \sqrt{8y}

2\sqrt[3]{3x^{2}}

\sqrt{xy^{2}}\cdot \sqrt{36}

6x\sqrt{2xy}

2\sqrt{3x^{2}}

6y\sqrt{x}

Problem 3 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

\frac{\sqrt[3]{3}}{\sqrt[3]{7}}

\sqrt{3\cdot 7}

\sqrt[3]{3\cdot 7}

\frac{\sqrt{3}}{\sqrt{7}}

\sqrt{3}\cdot \sqrt{7}

\sqrt[3]{3}\cdot \sqrt[3]{7}

\sqrt{\frac{3}{7}}

\sqrt[3]{\frac{3}{7}}

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Provide an example of a rational expression that includes an irrational denominator.

Take Note: Provide an example of a rational expression that includes a rationalized denominator.

Problem 5 Got It? Which answer choices in Problem 5 could have been eliminated immediately? Explain. Select all that apply.

A; There is a cube root in the numerator.

B; There is a cube root in the denominator. 

C; There is a cube root in the denominator. 

D; There is no y in the expression.

Solve It! You can cut the 36-square into four 9-squares or nine 4-squares. Which other n-square can you cut into sets of smaller squares in two ways?

A 64-square

A 49-square

An 18-square

Solve It! Is there a square you can cut into smaller squares in three ways? Explain.

Yes, any n-square where n is the product of three perfect squares can be cut into smaller squares in three ways.

No, this only works when n is a perfect square and only creates two ways in which to divied the n-square into squares.

Problem 2 Got It?

A

B

C

D

Problem 3 Got It?

A

B

C

D

Problem 5 Got It? Which answer choices in Problem 5 could have been eliminated immediately? Explain. Select all that apply.

A; There is a cube root in the numerator.

B; There is a cube root in the denominator. 

C; There is a cube root in the denominator. 

D; There is no y in the expression.

Algebra 2 6-2 Guided Practice: Multiplying and Dividing Radical Expressions

Algebra 2 6-2 Guided Practice: Multiplying and Dividing Radical Expressions

Problem 4 Got It? What is the simplest form of the expression?

Take Note: What is meant by rationalizing a denominator ?

Problem 5 Got It? What is the simplest form of the expression? Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not.

Problem 1 Got It? Can you simplify the expression? If so, simplify. If not, explain why not.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Classify each radical expression on the left.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Match each radical expression on the left with its simplest form on the right.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Use the properties of exponents and radicals to match equivalent expressions.

Problem 4 Got It? What is the simplest form of the expression?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is meant by rationalizing a denominator ?

Take Note: Provide an example of a rational expression that includes an irrational denominator.

Take Note: Provide an example of a rational expression that includes a rationalized denominator.

Problem 5 Got It? What is the simplest form of the expression? Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! You can cut the 36-square into four 9-squares or nine 4-squares. Which other n-square can you cut into sets of smaller squares in two ways?

Solve It! Is there a square you can cut into smaller squares in three ways? Explain.

Problem 2 Got It?

Problem 3 Got It?

Take Note: Provide an example of a rational expression that includes an irrational denominator.

Take Note: Provide an example of a rational expression that includes a rationalized denominator.

Problem 5 Got It? Which answer choices in Problem 5 could have been eliminated immediately? Explain. Select all that apply.

Problem 5 Got It? What is the simplest form of the expression?
Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Classify each radical expression on the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Problem 5 Got It? What is the simplest form of the expression?
Tip: Complicated rational expressions like this can be challenging to input unless you create the fraction bar first. To do that, type the forward-slash key before typing in the numerator and denominator.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?