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3 Roots and Radicals
In this chapter, you learn about square roots, cube roots, and so on.
Additionally, you learn about radicals and their relationship to roots. It is
important in algebra that you have a facility for working with roots and
radicals.
Squares, Square Roots, and Perfect Squares
You square a number by multiplying the number by itself. For instance, the
square of 4 is 444 = 16. Also, the square of − 4 is − 44 ⋅− = 16. Thus, 16 is
the result of squaring 4 or − 4. The reverse of squaring is fi nding the square
root. The two square roots of 16 are 4 and − 4. You use the symbol 16
to represent the positive square root of 16. Thus,
16 = 4. This number is the principal square root
of 16. Thus, the principal square root of 16 is 4. Using
the square root notation, you indicate the negative
square root of 16 as − 16. Thus, −= 16 −4.
Every positive number has two square roots that are equal in absolute
value, but opposite in sign. The positive square root is called the
principal square root of the number. The number 0 has only one square
root, namely, 0. The principal square root of
0 is 0. In general, if x is a real number such
that xxx=s, then sx (the absolute value
of x).
−≠ 16 − 4 ; − 16 is not a real
number because no real number
multiplies by itself to give − 16.
The symbol always gives one
number as the answer and that
number is nonnegative: positive or 0.
