Multiplying and Dividing Radical Expressions Quiz

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 $10\sqrt{14} = 10\sqrt{2}\sqrt{7}$.