Multiplying and Dividing Radical Expressions Quiz
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Questions and Answers

When can you use the Product Raised to a Power Rule to multiply radical expressions?

  • When the roots are the same (correct)
  • When the roots are different
  • When the index on all the radicals match
  • When the index on the radicals differ

    • What is the result of multiplying $\sqrt{12}$ and $\sqrt{27}$ using the Product Raised to a Power Rule?

  • $6\sqrt{3}$
  • $12\sqrt{3}$
  • $6\sqrt{6}$ (correct)
  • $18\sqrt{2}$

    • Can you use the Product Raised to a Power Rule to multiply a square root and a cube root?

  • Yes, always
  • Yes, if the numbers under the roots are prime
  • No, never
  • No, unless the index on both radicals match (correct)

    • What is the result of multiplying $\sqrt{20}$ and $\sqrt{45}$ using the Product Raised to a Power Rule?

    <p>$30\sqrt{3}$</p> Signup and view all the answers

    What is the result of multiplying $\sqrt{16}$ and $\sqrt{50}$ using the Product Raised to a Power Rule?

    <p>$40\sqrt{2}$</p> Signup and view all the answers

    What is the result of multiplying $5 oot 3 imes 2 oot 3$ using the Product Raised to a Power Rule?

    <p>$10 oot 3$</p> Signup and view all the answers

    What is the product of $3 oot 4$ and $4 oot 2$ using the Product Raised to a Power Rule?

    <p>$12 oot 6$</p> Signup and view all the answers

    What is the result of multiplying $2 oot 5$ and $3 oot 5$ using the Product Raised to a Power Rule?

    <p>$6 oot 5$</p> Signup and view all the answers

    What is the product of $2 oot 6$ and $3 oot 3$ using the Product Raised to a Power Rule?

    <p>$6 oot 18$</p> Signup and view all the answers

    What is the result of multiplying $4 oot 7$ and $2 oot 7$ using the Product Raised to a Power Rule?

    <p>$8 oot 7$</p> Signup and view all the answers

    What is the result of multiplying $3 oot 3 imes 5 oot 3$ using the Product Raised to a Power Rule?

    <p>$15 oot 3$</p> Signup and view all the answers

    What is the result of multiplying $2 oot 5 imes 4 oot 5$ using the Product Raised to a Power Rule?

    <p>$8 oot 5$</p> Signup and view all the answers

    What is the result of multiplying $2 oot 2 imes 3 oot 3$ using the Product Raised to a Power Rule?

    <p>$6 oot 6$</p> Signup and view all the answers

    What is the result of multiplying $4 oot 6 imes 7 oot 6$ using the Product Raised to a Power Rule?

    <p>$28 oot 6$</p> Signup and view all the answers

    What is the result of multiplying $5 oot 7 imes 2 oot 2$ using the Product Raised to a Power Rule?

    <p>$10 oot 7$</p> Signup and view all the answers

    Study Notes

    Product Raised to a Power Rule

    • The Product Raised to a Power Rule can be used to multiply radical expressions.
    • The rule does not specify the type of root (square, cube, etc.), but it is only applicable when the roots being multiplied are of the same type (e.g., both square roots).

    Multiplying Radical Expressions

    • Multiplying $\sqrt{12}$ and $\sqrt{27}$ using the Product Raised to a Power Rule results in $\sqrt{324} = 18$.
    • Multiplying $\sqrt{20}$ and $\sqrt{45}$ using the Product Raised to a Power Rule results in $\sqrt{900} = 30$.
    • Multiplying $\sqrt{16}$ and $\sqrt{50}$ using the Product Raised to a Power Rule results in $\sqrt{800} = 20\sqrt{2}$.
    • Multiplying $5\sqrt{3}$ and $2\sqrt{3}$ using the Product Raised to a Power Rule results in $10\cdot3 = 30$.
    • Multiplying $3\sqrt{4}$ and $4\sqrt{2}$ using the Product Raised to a Power Rule results in $6\sqrt{8} = 12\sqrt{2}$.
    • Multiplying $2\sqrt{5}$ and $3\sqrt{5}$ using the Product Raised to a Power Rule results in $6\cdot5 = 30$.
    • Multiplying $2\sqrt{6}$ and $3\sqrt{3}$ using the Product Raised to a Power Rule results in $6\sqrt{18} = 18\sqrt{2}$.
    • Multiplying $4\sqrt{7}$ and $2\sqrt{7}$ using the Product Raised to a Power Rule results in $8\cdot7 = 56$.
    • Multiplying $3\sqrt{3} \times 5\sqrt{3}$ using the Product Raised to a Power Rule results in $15\cdot3\sqrt{3} = 45\sqrt{3}$.
    • Multiplying $2\sqrt{5} \times 4\sqrt{5}$ using the Product Raised to a Power Rule results in $8\cdot5\sqrt{5} = 20\sqrt{5}$.
    • Multiplying $2\sqrt{2} \times 3\sqrt{3}$ using the Product Raised to a Power Rule results in $6\sqrt{6} = 6\sqrt{2}\sqrt{3}$.
    • Multiplying $4\sqrt{6} \times 7\sqrt{6}$ using the Product Raised to a Power Rule results in $28\cdot6 = 168$.
    • Multiplying $5\sqrt{7} \times 2\sqrt{2}$ using the Product Raised to a Power Rule results in $10\sqrt{14} = 10\sqrt{2}\sqrt{7}$.

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    Description

    Test your skills on multiplying and dividing radical expressions with this quiz. Assess your understanding of the product rule of radicals and practice simplifying expressions involving radicals.

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