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Unit 3B Radical Expressions and Rational Exponents

Unit 3B Radical Expressions and Rational Exponents. Radicals. Radical Expressions. Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical or the radical sign. radical sign. index. radicand.

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Unit 3B Radical Expressions and Rational Exponents

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  1. Unit 3B Radical Expressions and Rational Exponents

  2. Radicals Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical or the radical sign radical sign index radicand The expression under the radical sign is the radicand. The index defines the root to be taken.

  3. Radicals Radical Expressions The above symbol represents the positive or principal root of a number. The symbol represents the negative root of a number.

  4. Radicals Square Roots A square root of any positive number has two roots – one is positive and the other is negative. If a is a positive number, then is the positive square root of a and is the negative square root of a. Examples: non-real #

  5. Radicals Rdicals Cube Roots A cube root of any positive number is positive. A cube root of any negative number is negative. Examples:

  6. Radicals nth Roots An nth root of any number a is a number whose nth power is a. Examples:

  7. Radicals nth Roots An nth root of any number a is a number whose nth power is a. Examples: Non-real number Non-real number

  8. Rational Exponents The value of the numerator represents the power of the radicand. The value of the denominator represents the index or root of the expression. Examples:

  9. Rational Exponents More Examples: or

  10. Rational Exponents or or Examples: or

  11. Rational Exponents Use the properties of exponents to simplify each expression

  12. Simplifying Rational Expressions Product Rule for Square Roots Examples:

  13. Simplifying Rational Expressions Quotient Rule for Square Roots Examples:

  14. Simplifying Rational Expressions

  15. Simplifying Rational Expressions Examples:

  16. Simplifying Rational Expressions Examples:

  17. Simplifying Rational Expressions One Big Final Example

  18. Adding, Subtracting, Multiplying Radical Expressions Review and Examples:

  19. Adding, Subtracting, Multiplying Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

  20. Adding, Subtracting, Multiplying Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

  21. Adding, Subtracting, Multiplying Radical Expressions

  22. Adding, Subtracting, Multiplying Radical Expressions

  23. Adding, Subtracting, Multiplying Radical Expressions

  24. Dividing Radical Expressions

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