Multiplying Radicals with the Same Index

What is the basic rule for multiplying radicals with the same index?

• Multiply the radicands and keep the index.

• Add the radicands and change the index.

• Multiply the radicands and change the index.

• Add the radicands and keep the index.

In Example 1, what is the simplified form of the square root of 45?

• 5 square root of 9

• 9 square root of 5

• 3 square root of 5

• 5 square root of 3

How do you handle coefficients when multiplying radicals with the same index?

• Multiply the coefficients and multiply the radicands.

• Add the coefficients and add the radicands.

• Add the coefficients and multiply the radicands.

• Multiply the coefficients and add the radicands.

In Example 2, what is the result of multiplying 3 square root of 5 and square root of 2?

• 3 square root of 15

• 5 square root of 10

• 3 square root of 10

• 3 square root of 7

What is the cube root of 8?

• 1

• 4

• 2

• 3

In Example 3, what is the final result of multiplying negative six cube root of 3 and cube root of 4?

• Negative 6

• Negative 8

• Negative 10

• Negative 12

How do you simplify radicals with variables?

• Add the variables and simplify.

• Subtract the variables and simplify.

• Multiply the variables and simplify.

• Factor out perfect squares and simplify.

In Example 4, what is the simplified form of the square root of 32x^3y^3?

• 8x^2y^2 square root of 2xy

• 8xy square root of 2xy

• 4xy square root of 2xy

• 4x^2y^2 square root of 2xy

What property is used when multiplying a monomial by a binomial?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

In Example 5, what is the result of multiplying square root of 5 by (2 + square root of 5)?

• 5 square root of 5 + 10

• 2 square root of 5 + 5

• 2 square root of 5 + 10

• 5 square root of 5 + 5