Module 4: Radical Expressions

To determine the principal square root of a number that is not a perfect square you have two options. You can find a decimal approximation of the square root or you can represent the value in simplest radical form. In this module, you will learn how to represent square roots and cube roots in simplest form. You will also learn how to add, subtract, and multiply square roots and cube roots.

Getting Started

A tsunami is a group of large and forceful waves caused by a powerful earthquake, landslide, underwater explosion, or volcanic eruption. It differs from the waves you may have observed on the beach, which are caused by wind blowing across the ocean’s surface. A tsunami is much more vigorous than these types of waves, and its length is much longer than its depth. Scientists use mathematics and science principles to determine when conditions are favorable for a tsunami to develop. This enables them to provide warnings to the public, so that people can take the necessary precautions to ensure their safety.

One of the formulas scientists use to predict the arrival time of an approaching tsunami is s = √g · d, where s represents the speed of the tsunami, g represents the acceleration due to gravity, and d represents the depth of the water. Notice that this equation contains a radical expression, √g · d. Once scientists determine the speed of the tsunami, they can send out approximate warning times to coastal areas that could be affected by the waves, based on where the tsunami originated. Consider that a tsunami traveling 890 kilometers per hour can cross the entire Pacific Ocean in less than one day. Consequently, scientists’ use of the equation is extremely important.

In this module, you will learn how to simplify radical expressions so that you will be able to solve radical equations in your later studies of mathematics and science.

Key Vocabulary

To view the definitions for these key vocabulary terms, visit the course glossary.