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Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

## Radicals - To Exponential Form

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Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## Radicals - Cube Roots

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Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.  This lesson uses division.

## Radicals - Rational and Irrational Algebraic Terms

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## Radical Expressions - Conjugates Pairs

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

## Radicals - Rational and Irrational Numbers

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## Radicals - Adding and Subtracting Rational Expressions

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Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## Radicals - To Exponential Form with Variables

00:00

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
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