Radical Expressions Part 1

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Ch. 8 Radical Expressions Radical Expressions are
expressions with square roots in them. The square
root sign (v) is also called the radical
sign. The number or variable expression under
the radical sign is called the radicand. The
principal square root of a number is a positive
number that when squared becomes the
radicand. Because 72 49. -7 is also a square
root of 49 because (-7)2 49. But since -7 is
not positive, it is not the principal square
root. To indicate the negative square root you
have to attach a negative sign to the radical
sign. Simplifying Square Roots Radical
Expressions are in simplest form when the
radicand contains no factors that are perfect
squares. The Product Property of Square Roots
says you can split a radical expression into its
factors. Example 2 Simplify Are there
any factors of 18 that are perfect squares?
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Another definition of a square root is the power
½ . Taking a number or variable expression to
the power ½ is the same as taking the square
root.
IMPORTANT!!!!!!
WRONG!!
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What if the exponent isnt even? How do you take
the ½ th power of an odd exponent? Factor the
expression into factors with even powers and
factors with odd powers. Example Simplify
Simplify First factor out any perfect squares
of the coefficent, and then factor out even
powers of the variables.
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Higher Roots
the nth root of a to the nth power
Perfect Powers
a a2 a3 a4 a5
1 1 1 1 1
2 4 8 16 32
3 9 27 81 243
4 16 64 256 1,024
5 25 125 625 3,125
6 36 216 1,296 7,776
7 49 343 2,401 16,807
8 64 512 4,096 32,768
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APPLICATIONS Pythagorean Theorem
C (hypotenuse)
A (leg)
B (leg)
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Addition and Subtracting Radical
Expressions Adding and subtracting radical
expressions is like combining like terms. You
cannot add radical expressions that have
different terms inside the radical sign.
Therefore, if terms have different numbers inside
the radical sign and these radical expressions
cannot be simplified any more, then you cannot
combine them. You can, however, use the
distributive property to factor out any like
terms. Simplify Simplify