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pg 59­R.7­Radical Expressions
Radical Notation for Suppose that a is a real number, n is a positive integer, and is a real number.
Radical Notation for Suppose that a is a real number, m is an integer, n is a positive integer, and is a real number.
Radical, radicand, index
1
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Write each root using exponents and evaluate.
1) 2) 3) 4) 5)
6) 2
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Write in radical form and simplify. Assume all variable expressions represent positive real numbers.
7) 8) 9)
10) 11) 12) 13) 3
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CAUTION: It is not possible to "distribute" exponents over a sum.
Write in exponential form. Assume all variable expressions represent positive real numbers.
14) 15) 16) 17)
18) 4
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Evaluating
If n is an even positive integer, then
If n is an odd positive integer, then
Simplify each expression.
19) 20) 21) 22) 5
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23) 24) 25) 6
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Rules for Radicals
Suppose that a and b represent real numbers, and m and n represent positive integers for which the indicated roots are real numbers.
Product Rule
Quotient Rule
Power Rule 7
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Simplify. Assume all variable expressions represent positive real numbers.
26) 27) 28) 29) 30)
8
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31) Simplified Radicals
An expression with radicals is simplified when all of the following conditions are satisfied.
1) The radicand has no factor raised to a power greater than or equal to the index.
2) The radicand has no fractions.
3) No denominator contains a radical
4) Exponents in the radicand and the index of the radical have greatest common factor 1.
5) All indicated operations have been performed (if possible)
9
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Simplify each radical.
32) 33) 34) You can only add and subtract like radicals. Like radicals have the same index and radicand.
like radicals (ie
unlike radicals (ie 10
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Add or subtract, as indicated. Assume all variables represent positive real numbers.
35) 36) 37) 11
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Simplify each radical.
38) 39) 40) 12
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Find each product.
41) 42) 13
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Rationalize each denominator.
43) 44) 45) 14
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Simplify each expression. Assume all variables represent positive real numbers.
46) 47) 15