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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 What is the square root of 12 ( Ö 12 )? The square root of 12 is somewhere 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 Ö n = n Powers that are fractions represent roots of the coefficient |
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Revised: June 06, 2015