AnswersAA - F26 Advanced AlgebraDividing Radicals

Dividing Radicals Answers

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What is in simplest form? Assume and .

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What is in simplest form?

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What is in simplest form, where ?

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What is the simplest form of

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3x
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3x3
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What is the simplest form of

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Which expression should you multiply the numerator and denominator of by to rationalize the denominator?

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What is the simplest form of

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xy6
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x9y9
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The gravitational force formula is where F is the force between two objects, G is the constant of gravitation, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance between the objects. By rewriting the formula as , you can find the distance between objects. Which of the following gives the distance, r, in simplest form?

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The quotient property of radicals requires the indices of the radicals to be the same. Does this mean that it is not possible to write as a single radical? Explain.

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No, it is still possible to write the expression as a single radical. Because the radicands are powers of the same base (y), they can be rewritten using rational exponents as y^(3/4) and y^(1/2). By finding a common denominator for the exponents and subtracting them (3/4 - 2/4 = 1/4), the expression simplifies to y^(1/4), which is the 4th root of y.

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What is the simplest form of ?

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What is in exponential form?

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Did your explanation include the following?

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The radicands are powers of the same base, so they can be written using rational exponents.
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Simplify the quotient of the exponential expressions by getting a common denominator and subtracting exponents.
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The simplified expression is the 4th root of y.
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