1.6 Roots and Radicals

  • Principal nth 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  − 3 is an answer. Therefore, either 3 or  − 3 is a square root of 9 since 32 = 9 and ( − 3)2 = 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 a .  This means 9 = 3 and not  − 3.

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