# 1.6 Roots and Radicals

**Principal**`n`th Root • Simplifying Radicals • Using a Calculator • Imaginary Numbers

At times, we have to find the *square root* of a number, or maybe some other root of a number, such as a *cube root*. This means we must find a number that when squared, or cubed, and so on equals some given number. For example, to find the square root of 9, we must find a number that when squared equals 9. In this case, either 3 or $\hspace{0.17em}-\hspace{0.17em}3$ is an answer. Therefore, *either 3 or* $\hspace{0.17em}-\hspace{0.17em}3$ *is a square root of 9 since* ${3}^{2}\hspace{0.17em}=\hspace{0.17em}9$ and ${(\hspace{0.17em}-\hspace{0.17em}3)}^{2}\hspace{0.17em}=\hspace{0.17em}9.$

To have a general notation for the square root and have it represent *one* number, *we define the* **principal square root** *of a to be positive if a is positive and represent it by* $\sqrt{a}\hspace{0.17em}.\hspace{0.17em}$ This means $\sqrt{9}\hspace{0.17em}=\hspace{0.17em}3$ and not $\hspace{0.17em}-\hspace{0.17em}3.$

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