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Chapter 5—Powers, Exponents, and Roots 5-2 Square Roots and Cube Roots
Introducing Square Roots
Those are examples of finding
The square-root operation is the opposite of the squaring operation: - The square of 3 is 9 (3
^{2}= 9) - The square root of 9 is 3
If you can find the square of a number, you should be able to determine the square root of the result. The symbol for the square root of a number is theÖ . radical sign, Examples - 1. Since 12
^{2}= 144, then Ö 144 = 12 - 2. Since 25
^{2}= 625, then Ö 625 = 25 - 3, Since 100
^{2}= 10000, then Ö 10000 = 100
Examples & Exercises
Finding the Square Root of Any Real Number So far in this lesson, you've been finding the square root of a particular set of integers called perfect squares. A perfect square is an integer that is found by squaring another integer. You already know how to find the square root of 25 because it is a perfect square: 5 x 5 = 25, or you could write it as 5 Back in the "old days," math students had to learn how to calculate square roots with a complicated procedure that worked something like a combination of long division and factoring. A slide rule made matters a lot simpler. There were long tables of square-root values. Or if you knew how to use logarithms, you could find square roots that way, too. But things are much different today. The key to finding the square root of any number--whole number, fraction, decimal--is a calculator key. Calculator square-root key To find the square root of any number, simply key in the number (the radicand) and press the square-root key. Examples & Exercises
Introducing Cube Roots
These are examples of finding
The symbol for the cube root of a number is the radical sign with a little 3 that indicates the cube root: The cube-root operation is the opposite of the cubing operation: - The cube of 3 is 27 (3
^{2}= 27) - The cube root of 27 is 3
If you can find the cube of a number, you should be able to determine the cube root of the result.
Examples - 1. Since 4
^{3}= 64, then 64 = 4 - 2. Since –5
^{3}= –125, then –125 is –5 - 3, Since 10
^{3}= 1000, then 1000 = 10
Examples & Exercises
Using a Calculator to Find Cubes and Cube Roots You should be able to do a few, smaller-value cubes and cube roots in your head. But most of the time, however, you will need to use a calculator—especially for finding cube roots.To find the cube root of any number, simply key in the number (the radicand) and press cube-root key. On most calculators, the cube-root function is a 2nd level function. This means you have to press the 2nd key before pressing the key for the 2nd-level key. Examples & Exercises
Rewriting Roots in Exponent Form In previous lessons, you learned that a number multiplied by itself can be written with "square" notation. If that number is any number
Likewise:
- n = n
^{1/3} - Ö n = n
^{½}
Powers that are fractions represent roots of the coefficient |
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