8.2 Simplifying Radical Expressions
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Unit: Roots and Radicals
Module: Simplifying Radical Expressions
Simplifying Radicals
• •
A negative exponent tells you to treat its base as a fraction and flip it over. Then the exponent becomes positive. When dealing with rational exponents: • the numerator tells you to raise the base to the indicated power. • the denominator tells you to find the indicated root.
This work involves remembering the things we’ve recently been learning. The negative exponent means flip the number over. Once you flip, the exponent becomes positive.
The denominator of the rational exponent asks for the root, i.e., the number that produced each of these bases. Figure that out and your new base will have a whole number exponent, i.e., the original numerator.
Raise your new base to the power indicated by the exponent and you’re done.
This is a great example of how using rational exponents can vastly simplify even a horrible-looking problem. Notice that applying the rational exponent to each factor resulted in small numbers so the actual multiplication was simple arithmetic.
www.thinkwell.com
[email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved.
6565 –rev 08/03/2001
1
Unit: Roots and Radicals
Module: Simplifying Radical Expressions
[Page 1 of 1]
Simplifying Radical Expressions with Variables
• • •
A radical is asking for a root. It can be rewritten with the base number taken to a rational exponent whose denominator is the root requested. Raising a number at one power to another power is done by multiplying the two exponents. Grouping terms with a common exponent can show prospects for canceling and simplifying the problem.
Converting radicals to rational exponents sometimes makes it easier to see how to simplify your problem – especially if you apply the rational exponent separately to each term in the expression. Try to get comfortable expressing the powers and roots either way. It helps you see connections.
Some of the ugliest numbers you’ll ever see are these radical monsters. This one already looks simpler just by switching to rational exponents and grouping the numbers under a common exponent. Now, begin to cancel and simplify wherever you see an opportunity. Remember: 1. Write large and neatly so you can cancel easily. 2. Write the results after each set of changes. This helps prevent mistakes. You have the choice of writing your answer with either rational exponents or radical signs. They are equivalent and either way is OK.
www.thinkwell.com
[email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved.
6851 –rev 05/18/2001
2
Module: Simplifying Radical Expressions
Simplifying Radicals
• •
A negative exponent tells you to treat its base as a fraction and flip it over. Then the exponent becomes positive. When dealing with rational exponents: • the numerator tells you to raise the base to the indicated power. • the denominator tells you to find the indicated root.
This work involves remembering the things we’ve recently been learning. The negative exponent means flip the number over. Once you flip, the exponent becomes positive.
The denominator of the rational exponent asks for the root, i.e., the number that produced each of these bases. Figure that out and your new base will have a whole number exponent, i.e., the original numerator.
Raise your new base to the power indicated by the exponent and you’re done.
This is a great example of how using rational exponents can vastly simplify even a horrible-looking problem. Notice that applying the rational exponent to each factor resulted in small numbers so the actual multiplication was simple arithmetic.
www.thinkwell.com
[email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved.
6565 –rev 08/03/2001
1
Unit: Roots and Radicals
Module: Simplifying Radical Expressions
[Page 1 of 1]
Simplifying Radical Expressions with Variables
• • •
A radical is asking for a root. It can be rewritten with the base number taken to a rational exponent whose denominator is the root requested. Raising a number at one power to another power is done by multiplying the two exponents. Grouping terms with a common exponent can show prospects for canceling and simplifying the problem.
Converting radicals to rational exponents sometimes makes it easier to see how to simplify your problem – especially if you apply the rational exponent separately to each term in the expression. Try to get comfortable expressing the powers and roots either way. It helps you see connections.
Some of the ugliest numbers you’ll ever see are these radical monsters. This one already looks simpler just by switching to rational exponents and grouping the numbers under a common exponent. Now, begin to cancel and simplify wherever you see an opportunity. Remember: 1. Write large and neatly so you can cancel easily. 2. Write the results after each set of changes. This helps prevent mistakes. You have the choice of writing your answer with either rational exponents or radical signs. They are equivalent and either way is OK.
www.thinkwell.com
[email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved.
6851 –rev 05/18/2001
2
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