Topic: Simplifying Radical Expressions

 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 4 th power” of 2).

 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.

 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 x 2 isn’t inside.

 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

Apply the rule for a fractional exponent m/n. Simplify the exponent. 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 Simplify.

 Simplify the expression. Since we have like bases, we can use the Product Law of Exponents. Simplify exponent, then simplify expression.

 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).

 Identify 3 things you already knew from the material in the PowerPoint.  Identify 2 new things you learned.  Identify 1 question you still have.

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