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Beginning Pre-Calculus for Game Developers by Boris Meltreger, John P. Flynt

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Radicals and Roots

In a previous section, you examined the fundamentals of using exponents. You can also express exponents as fractions, and when you do so you enter the realm of roots and radicals. To explore a root, begin with the notion that to discover the power of a number, you begin by multiplying the number by itself, as the discussion in Chapter 2 detailed:

a × a = a23 × 3 = 9The square of 3 is 9.
a × a × a = a33 × 3 × 3 = 27The cube of 3 is 27.

If you raise 3 by the power of 2, you obtain its square. If you raise 3 by the power of 3, you obtain its cube. Suppose now that you begin with 9 and 27. You ask the following questions:

  • Given 9, what number can you multiply by itself to arrive at 9? What is the square root of 9?

  • Given 27, what ...

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