Description

In previous subjects of mathematics, we've learned how to simplify radicals. Hee, we learn how to simplify, multiply, divide, add and subtract radicals containing algebraic expressions. We also learn new concepts such as rationalizing the denominator, solving equations containing radicals, and explore rational exponents and radicals.

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.