Simplifying Radicals & Solving Quadratic Equations

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 example (available for download in your online classroom) to complete this discussion. Please complete the following problems according to your assigned number. (Instructors will assign each student their number.)

On pages 575 – 577, do the following problem

Simplify each expression. Write your answers with positive exponents. Assume that all variables represent positive real numbers.

On pages 584 – 585, do the following problem

Find the product of each pair of conjugates.

• 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 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 solve quadratic equations by two main methods: factoring and using the quadratic formula. Read the following instructions in order and view the example to complete this discussion. Please complete the following problems according to your assigned number. (Instructors will assign each student their number.)

Use FACTORING to solve:

x2 – 16 = 0 

Use the QUADRATIC FORMULA to solve:

8 on p. 680 which is: Fill in the blank.

An equation that is quadratic after a substitution is quadratic in .

• For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.

• For the quadratic formula problem, be sure that you use readable notation while you are working the computational steps. Refer to the Inserting Math Symbols handout for guidance with formatting.

• Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.

• Incorporate the following four 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 your math work.
  • Quadratic formula
  • Factoring
  • Completing the square
  • Discriminant

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