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Unit 9 – radical Functions

Unit 9 – radical Functions. Topic: Simplifying Radical Expressions. Properties of real roots (make a note card). Product Property of Roots The n th root of a product is equal to the product of the n th roots. Ex.

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Unit 9 – radical Functions

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  1. Unit 9 – radical Functions Topic: Simplifying Radical Expressions

  2. Properties of real roots (make a note card) • Product Property of Roots • The nth root of a product is equal to the product of the nth roots. • Ex. • We’ve already been doing this with square roots; this just says we can do it with any root, we just need to make sure one of our factors is a perfect “whatever” power the root is (in this case, 16 is a perfect “to the 4th power” of 2).

  3. Properties of real roots (make a note card) • Quotient Property of Roots • The nth root of a quotient is equal to the quotient of the nth roots. • Ex. • Again, we’ve already seen this with square roots; when taking the root of a variable, divide the variable’s exponent by the root.

  4. Simplifying radical expressions using properties of real roots • Simplify the expression . Assume x is positive. We want to use Product Property of Roots, but we need a factor of 16 that is a perfect cube. 8 can come out the “house” since the cube root of 8 is 2. With the variable, if the exponent is divisible by the root, we can also take the variable out of the “house.” The exponent 2 & the root 3 right next to each other are kind of confusing, so it is probably better to write our answer as I close my “house” so I know x2 isn’t inside.

  5. Fractional Exponents (make a note card) • An exponent is the same as the nth root. • Ex. • An exponent is the same as the nth root raised to the mth power (or the nth root OF the mth power). • Ex. • or

  6. Write the given expression using fractional exponents. Simplify if possible. Apply the rule for a fractional exponent m/n. Simplify the exponent. Simplify.

  7. Write the given expression in radical form, and simplify. We have 2 options. We can square -125 then take the cube root of the result (YIKES!), or we can take the cube root of -125 then square the result (sounds much simpler). Take the cube root of -125. Simplify.

  8. Simplifying expressions with fractional exponents • Simplify the expression . Since we have like bases, we can use the Product Law of Exponents. Simplify exponent, then simplify expression.

  9. Simplifying expressions with fractional exponents • Simplify the expression . Since we have like bases, we can use the Quotient Law of Exponents. We can’t have negative exponents, so we use the Law of Negative Exponents to make the exponent positive. Apply the rule for the fractional exponent 1/n then simplify using Quotient Property of Roots (remember, a negative fraction means that ONLY the numerator is negative).

  10. Journal EntryTitle: Simplifying radicals 3-2-1 • Identify 3 things you already knew from the material in the PowerPoint. • Identify 2 new things you learned. • Identify 1 question you still have.

  11. Homework • Quest: Simplifying Radical Expressions • DUE Monday, 3/19 (A-day) or Tuesday 3/20 (B-day)

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