Nov 20 Simplifying Radical Expressions

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What is a radical expression?

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A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x is a radical expression.

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How do you simplify a radical expression?

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To simplify a radical expression, factor the number under the radical into its prime factors, and then simplify by taking out pairs of factors for square roots.

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What is the product property of square roots?

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The product property states that the square root of a product is equal to the product of the square roots: √(a*b) = √a * √b.

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What is the quotient property of square roots?

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The quotient property states that the square root of a quotient is equal to the quotient of the square roots: √(a/b) = √a / √b.

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How do you multiply two radical expressions?

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To multiply two radical expressions, use the product property of square roots: √a * √b = √(a*b) and then simplify if possible.

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What is the simplified form of √32?

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The simplified form of √32 is 4√2.

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What is the simplified form of √(a^4)?

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The simplified form of √(a^4) is a^2.

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How do you simplify √(121a^4b^6)?

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To simplify √(121a^4b^6), factor it as √(121) * √(a^4) * √(b^6) = 11 * a^2 * b^3 = 11a^2b^3.

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What does it mean to rationalize the denominator?

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Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

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What is the difference between a perfect square and a non-perfect square?

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A perfect square is a number that can be expressed as the square of an integer (e.g., 1, 4, 9, 16), while a non-perfect square cannot (e.g., 2, 3, 5).