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$a=b_{n}⇒bis ann_{th}root ofa $

In many cases, some numbers have more than one real $n_{th}$ root. For example, $9$ has two square roots, $3$ and $-3.$
$3_{2}=9and(-3)_{2}=9 $

In this case, the principal root of $9$ is the positive root $3,$ since it has the same sign as $9.$ In general, the principal $n_{th}$ root of a number $a$ is the $n_{th}$ root that has the same sign as $a.$ It is denoted by the radical symbol and $n$ is the index of the radical. $Principaln_{th}Root:na $

A special case is when $n$ is and odd number and $b$ is negative. In this situation, there will be no nonnegative root and the principal root is negative. Some examples of $n_{th}$ roots and its description can be seen below.

$n_{th}$ root | Description |
---|---|

$16 =4$ | $16 $ indicates the principal square root of $16.$ |

$-16 =-4$ | $-16 $ indicates the opposite of the principal square root of $16.$ |

$±16 =±4$ | $±16 $ indicates both square roots of $16.$ |

$3-125 =-5$ | $3-125 $ indicates the principal cube root of $-125.$ |

$5-243 =-3$ | $5-243 $ indicates the principal fifth root of $-243.$ |

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