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Math in Living C O L O R !!
To see Section 5.02 with explanations, examples, and exercises, click here!
5.02 Cube Roots and More
Basic Algebra: One Step at a Time. Page 403 - 412: #54, 58, 93, 94.
Dr. Robert J. Rapalje, Retired
Central Florida, USA
The expression
3x
is called the cube root of x, and it asks the question, "What
cubed would equal x?" Likewise,
4x
means the fourth root of x,
5x
means the
fifth root of x, etc. In general,
nx
means the nth root of x, where the radicand is
x, and the index of the radical is n.
The operations of square root, cube root, fourth root, etc. are actually inverse
operations for the operations of squaring, cubing, raising to the fourth power,
etc. When taking square roots in the last section, it was essential to be familiar
with the perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and 169.
Also, remember that the even powers (x2, x4, x6, x8, x10, etc.) were and are
perfect squares. Now, when taking a cube root, it is essential to be familiar with
(i.e., memorize them!!) the perfect cubes, and other powers, especially the
numbers 1, 8, 27, 64, and 125.
23 = 8 24 = 16 25 = 32
33 = 27 34 = 81
43 = 64
53 = 125
And again, the list goes on. However, these are the main numbers that we use,
and with which you need to be familiar. You really need to have the numbers 8,
27, 64, and 125 in your head before you continue this lesson!!
