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Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical Expressions. Multiplying. If there are two radicals being multiplied and they have the same root then the radicands are multiplied Always check to see if the radicals can be simplified before multiplying!. Dividing.

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Multiplying and Dividing Radical Expressions

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  1. Multiplying and Dividing Radical Expressions

  2. Multiplying • If there are two radicals being multiplied and they have the same root then the radicands are multiplied • Always check to see if the radicals can be simplified before multiplying!

  3. Dividing • If there are two radicals with the same root being divided then they can be combined under a single radical and the radicands can be divided • If the two radicands do not divide evenly then we must rationalize our denominator…

  4. Rationalizing the Denominator • Rewrite it so there are no radicals in any denominator and no denominators in any radicals • Multiply the denominator by something to make it a perfect root

  5. Examples! 

  6. Binominal radical expressions

  7. Adding and Subtracting Expressions • 1st: Simplify all expressions • Then combine like terms • If radicals have difference indexes then they are NOT like terms • If the radicands are different then they are NOT like terms

  8. Multiplying Expressions • Use FOIL for binominals and distribution for all others • Both the coefficients and the radicands are multiplied • After multiplication all radicals should be simplified

  9. Dividing Expressions (Rationalize Denominator) • When dividing… • Remember that no radicals can exist in denominators so they should be rationalized. • If we have a binominal, to rationalize we change the sign of the radical and multiply by it over itself.

  10. Examples! 

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