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Simplifying Radicals

Simplifying Radicals. Binomial Conjugate:. Binomial quantity that turns the expression into a difference of squares. [B]. Example 1 Binomials Conjugates. [A]. Example 2 : Use Binomials Conjugates to Rationalize. [A]. [B]. SPECIAL FRACTION EXPONENT :.

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Simplifying Radicals

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  1. Simplifying Radicals Binomial Conjugate: Binomial quantity that turns the expression into a difference of squares.

  2. [B] Example 1Binomials Conjugates [A]

  3. Example 2: UseBinomials Conjugates to Rationalize [A] [B]

  4. SPECIAL FRACTION EXPONENT: The exponent is most often used in the power of monomials. Examples: Do you notice any other type of mathematical symbols that these special fraction exponents represent?

  5. Special Fraction Exponents, , are more commonly known as radicals in which the N value represents the root or index of the radical. Index Radical Symbol Radicals: Radicand Note: The square root or ½ exponent is the most common radical and does not need to have the index written. Steps for Simplifying Square Roots Prime Factorization: Factor the Radicand Completely Write the base of all perfect squares (PAIRS) outside of the radical as product Everything else (SINGLES) stays under the radical as a product.

  6. Operations with Rational (Fraction) Exponents • The same operations of when to multiply, add, subtract exponents apply with rational (fraction) exponents as did with integer (whole) exponents • Hint: Remember how to find common denominators and reduce. 1) 2) 3) 4) 5) 6)

  7. Example 1: ChangeRational to Radical Form A] B] C] Radicals (Roots) and Rational Exponent Form Rational Exponents Property: OR OR Example 2: ChangeRadical to Rational Form A] B] C]

  8. Radicals Classwork # 1 – 4: Write in rational form. 1. 2. 3. 4. #5 – 8: Write in radical form. 5. 6. 7. 8.

  9. Radicals Classwork #2 Determine if each pair are equivalent statements or not. 1. 2. and and 3. 4. and and 6. 5. and and

  10. Simplifying Rational Exponents • Apply normal operations with exponents. • Convert to radical form. • Simplify the radical expression based on the index and radicand. 1. 2. 3. 4. 5. 6. 7. 8.

  11. Radicals Classwork #3 Simplify the following expressions into simplest radical form 2. 1. 3. 6. 5. 4.

  12. Change of Base (Index or Root) • Write the radicand in prime factorization form • REDUCE the fractions of Rational Exponents to rewrite radicals. 1. 2. 3. 3. 3. 4.

  13. Change of Base Practice Problems 3. 1. 2. 4. 5. 6.

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