When simplifying square roots, the first step is to write two separate square root symbols and sort out the factors in the radicand, placing the perfect square factors in the first square root and the "leftover" factors in the second radical. The second step is to perform the first square root. This is what I call the "radical two-step!" This lesson was from one of my Intermediate Algebra classes from about 1993.

Section 3.02 Adding/Subtracting Radicals (Square Roots!)

When adding or subtracting square roots, remember that you can NEVER combine UNLIKE radicals. Quantities inside the two radicals and the order of the radicals must be exactly the same in order to combine them. This lesson was from one of my Intermediate Algebra classes from about 1993.

Section 3.02 Multiplying Radicals

When multiplying radical expressions, remember to multiply what is "outside" the radicals and keep it "outside." Multiply what is "inside" the radicals (i.e., radicands) and keep this "inside" the radicals. Then, always simplify the resulting radicals as in the previous section. This video was circa 1993.

Section 3.03 Reducing Fractions with Radicals

Simplifying fractions with radicals is really the same as reducing fractions with algebraic expressions, except that radicals (square roots!) are involve. Remember to NEVER divide out TERMS in reducing fractions! You can ONLY divide out FACTORS! This is why the FIRST step in reducing fractions is to FACTOR completely!! This video is from an Intermediate Algebra class in about 1993.

Section 3.04 Rationalizing Monomial Denominators

Rationalizing a denominator means to eliminate the radical (square root!) from the denominator. There are a number of "tricks" (legal math operations that do not change the value of the fraction) that can be performed on the fraction that "clear" the radicals from the denominator and simplify the expression. Videos presented here from about 1993 explain how to rationalize monomial and binomial denominators. Another video explains how to rationalize denominators with cube roots.

Section 3.04 Rationalizing Cube Root Denominators

Section 3.04 Rationalizing Binomial Denominators

Rationalizing a denominator means to eliminate the radical (square root!) from the denominator. There are a number of "tricks" (legal math operations that do not change the value of the fraction) that can be performed on the fraction that "clear" the radicals from the denominator and simplify the expression. The "trick" for rationalizing a binomial denominator is to multiply numerator and denominator by the CONJUGATE of the denominator. Videos presented here are from about 1993.

Section 3.05 Fractional Exponents

When a quantity is raised to a fractional power, take the radical of the denominator, and raise to the power of the numerator. This video, from one of my Intermediate Algebra classes of about 1993, should make this easy to understand.

Section 3.05 Fractional Exponents with Negative Base Numbers

This video is a continuation of the previous video about Fractional Exponents. Remember that when a quantity is raised to a fractional power, take the radical of the denominator, and raise to the power of the numerator. This video, from one of my Intermediate Algebra classes of about 1993, should make this easy to understand. This video explains what happens if the base number is negative.

5.06 Introduction: Function Machines, Functional Notation

This video is coming soon!

5.06 Functions, Domain, and Range

In my explanation of Functions, Domain, and Range, I h

5.06 Functions, Domain, and Range

FDR from a Graph. Intermediate Algebra, Section 5.06

5.06 Functions, Domain, and Range

College Algebra, Section 2.07. FDR from an Equation.

5.06 Functions, Domain, and Range

College Algebra, Section 2.07. FDR from a Graph.

Something Fishy Here!

Rob and Jaden at Lake Underhill