15 Questions
When can you use the Product Raised to a Power Rule to multiply radical expressions?
When the roots are the same
What is the result of multiplying $\sqrt{12}$ and $\sqrt{27}$ using the Product Raised to a Power Rule?
$6\sqrt{6}$
Can you use the Product Raised to a Power Rule to multiply a square root and a cube root?
No, unless the index on both radicals match
What is the result of multiplying $\sqrt{20}$ and $\sqrt{45}$ using the Product Raised to a Power Rule?
$30\sqrt{3}$
What is the result of multiplying $\sqrt{16}$ and $\sqrt{50}$ using the Product Raised to a Power Rule?
$40\sqrt{2}$
What is the result of multiplying $5 oot 3 imes 2 oot 3$ using the Product Raised to a Power Rule?
$10 oot 3$
What is the product of $3 oot 4$ and $4 oot 2$ using the Product Raised to a Power Rule?
$12 oot 6$
What is the result of multiplying $2 oot 5$ and $3 oot 5$ using the Product Raised to a Power Rule?
$6 oot 5$
What is the product of $2 oot 6$ and $3 oot 3$ using the Product Raised to a Power Rule?
$6 oot 18$
What is the result of multiplying $4 oot 7$ and $2 oot 7$ using the Product Raised to a Power Rule?
$8 oot 7$
What is the result of multiplying $3 oot 3 imes 5 oot 3$ using the Product Raised to a Power Rule?
$15 oot 3$
What is the result of multiplying $2 oot 5 imes 4 oot 5$ using the Product Raised to a Power Rule?
$8 oot 5$
What is the result of multiplying $2 oot 2 imes 3 oot 3$ using the Product Raised to a Power Rule?
$6 oot 6$
What is the result of multiplying $4 oot 6 imes 7 oot 6$ using the Product Raised to a Power Rule?
$28 oot 6$
What is the result of multiplying $5 oot 7 imes 2 oot 2$ using the Product Raised to a Power Rule?
$10 oot 7$
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 $10\sqrt{14} = 10\sqrt{2}\sqrt{7}$.
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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