Simplifying Radicals and Radical Operations

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What is a radical?

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A radical is a symbol that represents the root of a number, typically the square root (√) or higher roots (like cube root, fourth root, etc.).

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What does it mean to simplify a radical?

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Simplifying a radical means to express it in its simplest form, removing any perfect squares (or higher powers) from under the radical sign.

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How do you combine like radicals?

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You can combine like radicals by adding or subtracting their coefficients if they have the same radicand (the number under the radical).

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What is a perfect square?

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A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.

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What is the principle of simplifying radicals?

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The principle involves breaking down the radicand into its prime factors and removing pairs of factors from under the radical.