Simplifying Radicals

Please follow the example 

Problem #1

Problem #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. Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.

· Principal root

· Product rule

· Quotient rule

· Reciprocal

· nth root

Refer to 

Inserting Math Symbols

 
 Download Inserting Math Symbols

for guidance with formatting. Be aware with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have √12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not.  Therefore, we must specify whether we mean it to say √(12) + 9  or  √(12 + 9), as there is a big difference between the two. This distinction is important in your notation.

Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or  “sqrt(12 + 9)” depending on what we needed it to say.

Your initial post should be at least 250 words in length.

In this discussion, you will simplify and compare equivalent expressions written both in radical

form and with rational (fractional) exponents. Read the following instructions in order and view

the MAT222 Week 3 Discussion Example Download MAT222 Week 3 Discussion Example to

complete this discussion. Please complete the following problems according to your assigned

number.

INSTRUCTOR GUIDANCE EXAMPLE: Week Three Discussion

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.

2(-4*1/2) The exponents multiply each other.
2-2 -4*1/2 = -2 so the new exponent is -2.
1
22 The negative exponent makes a reciprocal of base number and

exponent.
1 The final simplified answer is ¼. This is the principal root of the
4 square root of 2-4.

#63.

4

1

20

1281












y

x
The Power Rule will be used again with the outside exponent



















4

1
20

4

1
1

2

4

1
4

3

y

x
multiplying both the inner exponents. 81 = 34

5

33

y

x
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.

#89.

3

2

27

8







 First rewrite each number as a prime to a power.

3
2
3
3
3

2








 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.

 

3

2
3

3
2
3
3

2



3*2/3 = 2 in both numerator and denominator.

 

9

4
3

2
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.