Investigating Rational and Irrational Numbers Module Overview

Introduction

A rational number is a number that can be written as a fraction, or a ratio, of two numbers. When a rational is written in decimal form, the decimal will be a terminating or repeating decimal.

An irrational number, on the other hand, is a number that cannot be written as a fraction, or a ratio, of two numbers. If you were to write it as a decimal, it would be a non-terminating or non-repeating decimal.

In this module, we'll explore what happens when you add, subtract and multiply rational and irrational number with a special focus on square and cube roots.

Essential Questions

How do we know if numbers are rational or irrational?
What type of number will result when adding, subtracting, and multiplying irrational and rational numbers?
What are the various properties of square roots and cube roots?
How can we simplify square root and cube root expressions?
How can we take the square root and the cube root of a number?
How can we add, subtract and multiply square root and cube root expressions?

Key Terms

Base – The number used as a factor when raised to a power.

Coefficient - A number multiplied by a variable.

Exponent – The number used to indicate how many times the base is used as a factor.

Expression - A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Index – The number above the radical symbol used to indicate the exponent used in the root.

Irrational Number – A number that cannot be written as a fraction, terminating decimal or repeating decimal.

Perfect Square – The square of a whole number.

Power – A number produced by raising a number to an exponent.

Radical Expression - An expression containing a root. The most common radical functions are the square root and cube root functions,

Radical Symbol – The symbol used to represent the nonnegative square root of a number.

Rational Number – Any number that can be written as a fraction.

Root – The number used as a factor in radicals.

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