Simplifying Higher Radicals w/ Variables

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Define a higher radical.

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A higher radical is a root of a number or expression that is not a square root, such as cube roots (3rd roots), fourth roots, etc.

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What is the cube root of a number?

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What is the process of simplifying higher radicals with variables?

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To simplify higher radicals with variables, factor the expression under the radical into perfect powers and apply the root to those factors.

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Define perfect squares and perfect cubes in the context of radicals.

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Perfect squares are numbers that can be expressed as the square of an integer, while perfect cubes are numbers that can be expressed as the cube of an integer.

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What is the significance of simplifying radicals in algebra?

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Simplifying radicals makes expressions easier to work with and helps in solving equations more efficiently.