Section 1.2 Exponents and Radicals

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Section 1.2Exponents and Radicals

• Radicals and Rational Exponents

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Square Root of x
A square root is one of two identical
real numbers whose product is x.
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The product of two identical real numbers can
never equal a negative number.
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Cube Root of x
A cube root of a number is one of three identical
real numbers whose product is the number.
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The index of 3 indicates that 3 identical numbers
must be multiplied to equal x.
For example,
since
since
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In square root radicals the index is usually
omitted.
Therefore,
If no index is written next to the radical sign,
it is assumed to be 2.
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The nth Root of x
The nth root of a number is one of n identical
real numbers whose product is the number.
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A real number b is the nth root of x if and
only if b satisfies the equation
For example,
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not a real number so the nth root of x does not
exist.
For example,
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Properties of the nth root of x
if x ? 0
if x lt 0 and n is odd
if x lt 0 and n is even
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Principal nth Root
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For example,
Although the two square roots of 16 are 4 and
4, the principal square root of 16 is 4 since 4
has the same sign as 16.
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For example,
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where x is any real number, n is an integer, and
k is a positive integer.
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In evaluating expressions of the form
it is usually easier to first take the nth root
of x and then raise the result to the power m.
For example,
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Homework Assignment
1. Read Section 1.2 pages 19 20.
2. Do the following problems.
Page 25-26 s 35 56, 85 92 (all)
3. Complete worksheet.
4. Study for quiz on Monday.