{{ tocSubheader }}

{{ 'ml-label-loading-course' | message }}

{{ tocSubheader }}

{{ 'ml-toc-proceed-mlc' | message }}

{{ 'ml-toc-proceed-tbs' | message }}

An error ocurred, try again later!

Chapter {{ article.chapter.number }}

{{ article.number }}. # {{ article.displayTitle }}

{{ article.intro.summary }}

{{ 'ml-btn-show-less' | message }} {{ 'ml-btn-show-more' | message }} {{ 'ml-heading-abilities-covered' | message }}

{{ 'ml-heading-lesson-settings' | message }}

| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount}} |

| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount}} |

| {{ 'ml-lesson-time-estimation' | message }} |

Concept

$ 4_{2}=16 16 =±4⇕and (-4)_{2}=16 $

The principal root of $16$ is $4.$ In contrast, when considering odd roots, such as cube roots, there is only one real root, which then is the principal root. Since odd roots are defined for all real numbers, the principal root can be either negative or positive. Suppose that $n$ is an integer greater than $1$ and $a$ is a real number. $n$ is even | $n$ is odd | |
---|---|---|

$a>0$ | Two square roots: one positive and one negative. The principal root is the positive one. | One positive root, which is the principal root. |

$a=0$ | The only root is zero. | The only root is zero. |

$a<0$ | No real roots. | One negative root, which is the principal root. |

The principal root is an important concept that guarantees functions involving radicals are well-defined. For example, when defining the square root function as $f(x)=x ,$ it is implied that $f(x)$ returns the principal square root of $x.$ This is to guarantee that the function has a unique output for each input value.

Loading content