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.
Expressions That Have No Common Radical Factor
Simplifying a radical expression that has no common radical factor using subtraction.
Square Roots of Decimal Numbers and Perfect Square Decimals
Finding the square root of a decimal is discussed, noting that any decimal that does not have an even number of places after the decimal cannot have an exact square root.
Two Factoring Problems
Simplifying more complex radicals with numbers and variables.
Two Approaches for Dividing Radicals
Two approaches to simplifying radical expressions using division when the radical in the numerator and the radical in the denominator are perfect squares. Another guideline for simplifying radicals is introduced: all fractions must be reduced to low...
Solve: 3x(x - 2) = 14
The equation 3x(x - 2) = 14 is solved using the quadratic formula.