Math 104 Study Guide: Radicals, Rational Exponents, Simplifying, Solving Equations, Study notes of Algebra

This study guide for math 104 provides instructions for effective learning, followed by a detailed exploration of radicals and rational exponents, simplifying radical expressions, and solving radical equations. Students are encouraged to engage actively with the material through self-dialogue and seeking help when needed.

Typology: Study notes

Pre 2010

Uploaded on 08/19/2009

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Chapter 9
Study Guide
Math 104
1. Make time in your schedule to learn; you cannot take shortcuts.
2. Read each section in your textbook and answer the questions in the study
guide before you go to class.
3. Take notes in class, trying to understand as the teacher presents
examples and explains concepts.
4. Do your homework (It should be easier after the previous two steps).
Make sure to understand what you are doing and be able to solve each
problem completely and correctly by yourself.
5. Carry on a conversation with yourself as you work, asking as you start
each problem, “What is this? What is my goal? What should my answer look
like when I am done?” Then, as you work a problem ask, “What property
allows me to take this step?” And at the end, “ Does my answer make sense?
How can I check it?”
6. Maintain a great attitude about learning Algebra; people who have a good
attitude find it easier to learn, and those who learn algebra well usually
enjoy it.
7. Go to the lab or your instructor’s office and get help when you need it.
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Chapter 9

Study Guide

Math 104

  1. Make time in your schedule to learn; you cannot take shortcuts.
  2. Read each section in your textbook and answer the questions in the study guide before you go to class.
  3. Take notes in class, trying to understand as the teacher presents examples and explains concepts.
  4. Do your homework (It should be easier after the previous two steps). Make sure to understand what you are doing and be able to solve each problem completely and correctly by yourself.
  5. Carry on a conversation with yourself as you work, asking as you start each problem, “What is this? What is my goal? What should my answer look like when I am done?” Then, as you work a problem ask, “What property allows me to take this step?” And at the end, “ Does my answer make sense? How can I check it?”
  6. Maintain a great attitude about learning Algebra; people who have a good attitude find it easier to learn, and those who learn algebra well usually enjoy it.
  7. Go to the lab or your instructor’s office and get help when you need it.

Section 9.1 Radicals and Rational Exponents Read section 9.1, pages 514 - 520 and answer the following questions as you read:

  1. Explain in words what number is referred to by 3
  2. For the number 4 6 , what is the index and what is the radicand?
  3. If x = y^5 , then ____ is a _____ root of _____.
  4. Why isn’t the even root of a negative number a real number? Give an example of the even root of a negative number.
  5. List the first twelve perfect squares.
  6. List the first five perfect cubes.
  7. List the powers of two through 2^10 =

Section 9.2 Simplifying Radical Expressions Read section 9.2, pages 524 – 528 and answer the following questions as you read:

  1. Simplify the radical 3 250. Describe your strategy.
  2. Simplify 3 − 128 x^5 y^12
  3. List the three criteria that must be satisfied for a radical to be simplified.
  4. Simplify 3 5
  1. Simplify (^3 ) 3

ab

x

  1. Describe what two radicals must have in common before they can be combined through addition or subtraction.

Section 9.3 Multiplying and Dividing Radical Expressions Read section 9.3, pages 532 – 535 and answer the following questions as you read:

Section 9.4 Solving Radical Equations Read section 9.4, pages 540 – 545 and answer the following questions as you read:

Section 9.5 Complex Numbers Read section 9.5, pages 550 – 555 and answer the following questions as you read: