MAT 222: Intermediate Algebra


Discussion 1: Simplifying RadicalsThe last letter of my first name is A or L. On pages 576-577, do the following problems 42 and 101Problem 42 is 27- 2/3                          27- 1/3Problem 101 is (a 1/2 b) 1/2 (ab 1/2)*Simplify each expression using the rules of exponents and examine the steps you are taking.* Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing.1. Principal root2. Product rule 3. Quotient rule4. Reciprocal 5. nth rootMake sure you look at both example sheets, that I posted up. No plagiarism follow all directions for this post. MAT222.InsertingSymbolsJobAid.pdf , MAT222.W3.DiscussionExample.pdf


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Inserting Math Symbols
Throughout these courses MAT 221 and MAT 222 students are required to submit written assignments
in Microsoft Word that require the use of Mathematical symbols. Please follow the directions below in
order to insert mathematical symbols into your documents.
Inserting Symbols:
1. Click with your mouse in the space you would like the mathematical symbol to appear.
2. Click with your mouse on the “Insert” tab on the upper navigation toolbar.
3. Click with your mouse on the “Symbol” button.
4. In the dropdown menu, click with your mouse on “More Symbols”.
5. In the “Symbol” window, click on the “Subset” dropdown menu and choose the desired category
that fits the mathematical equation.
6. Select the desired symbol and click with your mouse “Insert”.
7. The symbol should appear in your document.
If you have any questions, please do not hesitate the contact your instructor.
Simplifying Radicals
1. Simplify each expression using the rules of exponents and explain the steps you
are taking.
2. Next, write each expression in the equivalent radical form and demonstrate how it
can be simplified in that form, if possible.
3. Which form do you think works better for the simplification process and why?
#51. (2-4)1/2
The exponent working on an exponent calls for the Power Rule.
The exponents multiply each other.
-4*1/2 = -2 so the new exponent is -2.
The negative exponent makes a reciprocal of base number and
The final simplified answer is ¼. This is the principal root of the
square root of 2-4.
? 81x 12 ? 4
#63. ?? 20 ??
? y ?
? 4? 14 12? 14
?3 x
? y 20? 4
3x 3
The Power Rule will be used again with the outside exponent
multiplying both the inner exponents. 81 = 34
4*1/4 = 1, 12*1/4 = 3, and 20*1/4 = 5
All inner exponents were multiples of 4 so no rational exponents are left.
? 8 ?3
#89. ? ? ?
? 27 ?
First rewrite each number as a prime to a power.
? 23 ? 3
?? ? 3 ??
? 3 ?
Use the Power Rule to multiply the inner exponents.
The negative has to be dealt with somewhere so I will put it with
the 2 in the numerator.
?? 2?3? 3
3*2/3 = 2 in both numerator and denominator.
?? 2?2
The squaring eliminates the negative for the answer.
It turns out that the examples I chose to work out here didn’t use all of the vocabulary
words and required one which wasn’t on the list. Students should be sure to use words
appropriate to the examples they work on.

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