Sections of this topic include:
1. Roots and Radicals
We begin by investigating finding roots of perfect squares and with variables. Groups of this section include finding roots; finding roots with variables; using calculators to approximate roots; solving applied problems using roots.
2. Simplified Forms of Radicals
After simplifying roots of perfect squares, the question arises of how to simplify roots that are not perfect squares? This section addresses that question. Groups in this section includes simplifying radicals; simplifying radical expressions; and using calculators to simplify radicals.
3. Addition and Subtraction of Radicals
Much like rational expressions or real numbers, we are curious how to perform operations with radicals. We begin by investigating addition and subtraction of radicals. Groups of this section include adding and subtracting radical expressions; simplifying fractions containing radicals.
4. Multiplication and Division of Radicals
Continuing our study of operations or radicals, we now investigate how to multiply and divide radicals. Groups of this section include multiplying and dividing radical expressions; multiplying and dividing radical expressions containing variables; rationalizing the denominator with radical expressions containing variables.
5. Solving Equations Containing Radicals
Improving our skills in solving equations, we explore how to solve equations that contain radicals. Groups in this section include solving equations containing radicals; using the distance formula; solving literal equations containing radicals.
6. Rational Exponents and Radicals
Combining laws of exponents with radicals, we explore the idea of having rational exponents in expressions. Groups in this section include writing expressions with rational exponents as radicals; writing radical expressions as expressions with rational exponents; simplifying expressions with rational exponents; using the product or quotient rules of exponents to simplify expressions.
