Simplifying by Adding or Subtracting Common Radical Factors
A new guideline for simplifying radicals is introduced: the terms in a fully-simplified radical expression must have no common radical factors. Simplifying a radical expression by adding or subtracting common radical factors is illustrated.
Multiplying First to Get a Perfect Square in the Radicand
Simplifying a radical by multiplying first to get a perfect square in the radicand.
Simplifying to Find a Common Radical Factor
The process of simplifying to find a common radical factor is demonstrated.
Simplifying Radicals before Multiplying
Instances are demonstrated where simplifying radicals before multiplying are indicated.
Square Root of a Product, The
Illustrations of the rule for multiplying radicals: the square root of a times the square root of b equals the square root of the product a times b.
Simplifying Rational Expressions
Simplifying rational expressions is like reducing rational numbers. First fully factor the numerator and denominator and then cancel all the common factors. The process is illustrated step by step.
Rational Expressions that Equal - 1
Rational expressions that equal -1 are recognizable: the terms in the numerator are identical to the terms in the denominator except for their signs, which are opposite.
Expressions That Have No Common Radical Factor
Simplifying a radical expression that has no common radical factor using subtraction.
Subtraction Problem That Requires Factoring, A
Solving a problem in which both denominators are quadratic trinomials is demonstrated.
Solving an Equation with the Least Common Denominator: Another Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.