Dr.Fraser begins the new section on Radical Expressions with Simplifying Radical Expressions. After a thorough introduction of radical expression simple forms as principal square roots, he teaches you the product rule. Then, after learning how to deal with square roots of variables with even powers, you will dive into the quotient rule, rationalizing denominators, and conjugates. At the end of this lecture are four additional examples on how to simplify expressions.
expression contains a square root. The expression inside the
square root is called a radicand.
To simplify a
radical expression, extract all perfect squares from the radicand.
Use the product
and quotient properties of square roots to help you simplify radical
If the exponent of
the variable inside the radical is even and the resulting simplified
expression has an odd exponent, take the absolute value of
the expression for the simplified expression to guarantee that it is
form, there can be no radicals in the denominator. Removing such
radicals is called rationalizing the denominator.
To rationalize a
monomial denominator, simply multiply the numerator and
denominator by the radical in the denominator.
To rationalize a
binomial denominator, multiply the numerator and denominator
by the conjugate of the denominator. The conjugate is the
same as the original binomial but with the sign between the first
term and the second term reversed.
To be in
simplified form, there must be no perfect squares or
fractions in the radicand and there must be no radicals in the
Simplifying Radical Expressions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.