We Can Often Multiply and Divide Radicals with Different Indexes $$\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$$

question 51

Multiple Choice

We can often multiply and divide radicals with different indexes.For example: $$\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$$
Use this idea to write the following expression as a single radical.
$$\sqrt { 4 } \sqrt [ 3 ] { 4 }$$

• A) \(\sqrt { 1024 }\)
• B) \(\sqrt [ 6 ] { 1024 }\)
• C) \(\sqrt [ 3 ] { 1024 }\)
• D) \(\sqrt [ 6 ] { 4 }\)
• E) \(\sqrt [ 6 ] { 256 }\)

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Definitions:

Expression

A combination of numbers, variables, and operations that together represent a particular value.

Positive Exponents

Represent numbers multiplied by themselves a certain amount of times, indicating a base raised to the power of a positive number.

Expression

A combination of numbers, variables, and mathematical operations that represents a particular value.

X

Often used in mathematics as a variable or unknown value in equations and algebraic expressions.