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

Last updated almost 3 years ago
25 questions
3

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

10

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?

10

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

Take Note: Take a moment to record the property Combining Radical Expressions: Products in your notes.
3

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

8

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

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

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

5

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

3

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

10

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.

  • 200
  • 4
  • 9
  • 144
  • 2
  • 3
  • 25
  • 7
  • 1
  • 21
  • Perfect square
  • NOT perfect square
10

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.

  • 1000
  • 125
  • 27
  • -64
  • 1
  • 4
  • -16
  • 9
  • 3
  • -8
  • Perfect cube
  • NOT perfect cube
9

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.

  • -3x\sqrt{5x^{2}}
  • -2\sqrt{3}
  • \sqrt{12}
  • \sqrt{24}
  • 2\sqrt{6}
  • 16b^{5}\sqrt{7b}
  • \sqrt{t^{5}}
  • \sqrt{3ab}
  • 4\sqrt{200}
  • In simplest form
  • NOT in simplest form
10

Problem 2 Got It?

3

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

8

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

Draggable itemCorresponding Item
\sqrt{xy^{2}}\cdot \sqrt{36}
2x\sqrt{3}
2\sqrt{3x^{2}}
2\sqrt[3]{3x^{2}}
3\sqrt{x^{3}}\cdot \sqrt{8y}
6x\sqrt{2xy}
\sqrt[3]{8x}\cdot \sqrt[3]{3x}
6y\sqrt{x}
10

Problem 3 Got It?

Take Note: Take a moment to record the property Combining Radical Expressions: Quotients in your notes.
3

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

8

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

Draggable itemCorresponding Item
\sqrt{3}\cdot \sqrt{7}
\sqrt{3\cdot 7}
\sqrt{\frac{3}{7}}
\frac{\sqrt{3}}{\sqrt{7}}
\sqrt[3]{3\cdot 7}
\sqrt[3]{3}\cdot \sqrt[3]{7}
\frac{\sqrt[3]{3}}{\sqrt[3]{7}}
\sqrt[3]{\frac{3}{7}}
10

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

3

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

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.

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.

10

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

10

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