Radicals and Rational Exponents Flashcard

Front

Define a radical expression.

Back

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}@@.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, @@x^{rac{m}{n}} = oot{n}{x^m}@@.

Front

Solve the radical equation @@ ext{ } oot{2}{x + 3} = 5@@.

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Back

@@ oot{2}{x}@@.

Front

What is the principal square root of a number?

Back

The principal square root of a number is the non-negative root of that number. For example, the principal square root of 9 is 3.

Front

Solve the equation @@ ext{ } oot{3}{x} = 4@@.

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Front

Convert the radical expression @@ oot{4}{y^2}@@ to an expression with a rational exponent.

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Front

What is the domain of a radical function?

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The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

Solve the equation @@ ext{ } oot{2}{x - 1} = 3@@.

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Front

Convert the expression @@ oot{5}{x^3}@@ to an expression with a rational exponent.

Back