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.
Multiplying Whole Numbers, Part 1: Summary: Multiplying Whole Numbers, Part One
This clip summarizes multiplication of whole numbers, including the relationship between addition and multiplication, the use of arrays, and the results when multiplying numbers by one or zero.
Multiplying Whole Numbers, Part 1: Identity For Multiplication, The
This clip explains that, just as zero is the identity for addition, the number 1 is the identity for multiplication because, any number, when multiplied by 1, "...isn't changed at all."
Multiplying Whole Numbers, Part 1: Arrays
This clip explains that one way to look at multiplication is through a pattern of columns and rows known as an array.
Multiplying Whole Numbers, Part 1: Multiplication By Zero
This clip explains that the product of any number multiplied by zero is zero.
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.
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.