Radical Flashcard

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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, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

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To simplify a fraction with radicals, multiply the numerator and denominator by the conjugate of the denominator.

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What is the extraneous solution in an equation?

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An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

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How do you convert an expression to radical form?

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To convert an expression to radical form, rewrite it using roots. For example, @@x^{rac{1}{2}} = ext{ } oot{2}{x}@@.

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What is the definition of a perfect square?

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A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16 are perfect squares.

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How do you identify the principal square root?

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The principal square root of a non-negative number is the non-negative value that, when squared, gives the original number.

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What is the product property of square roots?

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The product property states that @@ oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.

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What is the quotient property of square roots?

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The quotient property states that @@rac{ oot{n}{a}}{ oot{n}{b}} = oot{n}{rac{a}{b}}@@, provided that b is not zero.

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How do you solve equations involving radicals?

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To solve equations involving radicals, isolate the radical on one side and then square both sides to eliminate the radical.