RIN - Investigating Rational and Irrational Numbers Overview

Investigating Rational and Irrational Numbers Module Overview

calc.jpeg

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. 

 IMAGES CREATED BY GAVS