Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 39: Simplifying Radical Expressions
Answer/Discussion to 1a
Note that both radicals have an index number of 5, so we were able to put their product together under one radical keeping the 5 as its index number.
Since we cannot take the fifth root of and does not have any factors we can take the fifth root of, this is as simplified as it gets.
Answer/Discussion to 2a
*Use the quotient rule of radicals to rewrite
*Square root of 49 is 7
Since we cannot take the square root of 5 and 5 does not have any factors that we can take the square root of, this is as simplified as it gets.
Answer/Discussion to 3a
Even though 40 is not a perfect cube, it does have a factor that we can take the cube root of.
Check it out:
*Use the prod. rule of radicals to rewrite
*The cube root of 8 is 2
In this example, we are using the product rule of radicals in reverse to help us simplify the cube root of 40. When you simplify a radical, you want to take out as much as possible. The factor of 40 that we can take the cube root of is 8. We can write 40 as (8)(5) and then use the product rule of radicals to separate the 2 numbers. We can take the cube root of 8, which is 2, but we will have to leave the 5 under the cube root.
Answer/Discussion to 3b
Even though is not a perfect square, it does have a factor that we can take the square root of.
Check it out:
*Rewrite as
*Use the prod. rule of radicals to rewrite
*The square root of is
In this example, we are using the product rule of radicals in reverse to help us simplify the square root of. When you simplify a radical, you want to take out as much as possible.
The factor of that we can take the square root of is . We can write as and then use the product rule of radicals to separate the two numbers. We can take the square root ofwhich is, but we will have to leave the rest of it under the square root.
Answer/Discussion to 4a
*Simplify fraction
*Take the square root
Note that both radicals have an index number of 2, so we are able to put their quotient together under one radical keeping the 2 as its index number. Since the radicand is a perfect square, we are able to take the square root of the whole thing, which leaves us with nothing under the radical sign.
Last revised on July 19, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.
FAQs
Review And Practice
To pass intermediate algebra, it would behoove you to take time to practice basic algebra before this advanced course. Reviewing these fundamentals will ensure you have a solid grasp of the math concepts that intermediate algebra is built on.
What grade is intermediate algebra taught? ›
The California Community College and Intermediate Algebra
| 1 | 2 |
|---|
| Algebra I Elementary Algebra Beginning Algebra | Algebra II Intermediate Algebra |
| Typically 8th or 9th grade OR community college basic skills | Typically 10th or 11th grade OR community college, but not a baccalaureate level course |
Study Hard
Complete all of your assigned homework. You can also consider working on the extra practice problems in your textbook. The more algebra problems you solve, the better prepared you'll be for your exams. Give yourself enough time to work on homework and to prepare for exams.
How to break down algebra problems? ›
How to Solve an Algebra Problem
- Step 1: Write Down the Problem. ...
- Step 2: PEMDAS. ...
- Step 3: Solve the Parenthesis. ...
- Step 4: Handle the Exponents/ Square Roots. ...
- Step 5: Multiply. ...
- Step 6: Divide. ...
- Step 7: Add/ Subtract (aka, Combine Like Terms) ...
- Step 8: Find X by Division.
Study Effectively
Make sure you're completing your assigned readings and all the practice problems your instructor gives you. It's a good idea to work on some of the unassigned problems in your book, as well, especially if you're having trouble understanding a particular type of problem and to get more practice.
What is intermediate algebra equal to? ›
Approximately equivalent to 2nd-year high school algebra. Course goals (gain a good understanding of the following concepts): Properties of real numbers; operations on real numbers; fractions; order of operations.
Is algebra 1 in 9th grade bad? ›
In fact, one study showed that students that take algebra in 9th grade as opposed to 8th grade are more likely to take four years of high school math and continue taking math classes in college.
What is harder, college algebra or intermediate algebra? ›
For me personally, College Algebra seemed like a repeat of Int. Algebra with a few more topics added to it. I didn't think it was much harder. I had it done in 2 weeks with about 6-7 hours per weekday.
Should 8th graders take algebra 1? ›
Although taking Algebra 1 in eighth grade or even seventh grade can put students on track to take calculus before they complete high school, it's important to note that not everyone is ready to take Algebra 1 in middle school.
How many students fail algebra? ›
Overall, 82% of the ninth-grade students passed Algebra I in their ninth-grade year, 5% recovered the Algebra I credit early in their high school career (by the end of their second year), 3% recovered the Algebra I credit later in their high school career (after their second year but by the end of their fourth year), ...
The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to dropping out of college.
Is algebra easier than calculus? ›
Calculus is the hardest mathematics subject and only a small percentage of students reach Calculus in high school or anywhere else. Linear algebra is a part of abstract algebra in vector space. However, it is more concrete with matrices, hence less abstract and easier to understand.
Why am I so weak in algebra? ›
The primary cause of math difficulties is an inability to create a gestalt image for the concepts underlying math processes. Individuals often attempt to memorize facts instead of being able to think, reason, and problem solve with numbers.
Why do most students fail algebra? ›
Algebra is overwhelming for many students because it's the first math class they take where they must wrestle with variables, abstract concepts, and creative problem solving. And there's often not enough done in the classroom to connect Algebra to their everyday lives and explain why it's worth understanding.
What is the hardest topic in algebra? ›
Top-Five Most Difficult Algebra Concepts
- 1) - Multiplying Polynomials by Monomials.
- 2) - Modeling Using Exponential Functions.
- 3) - Averaging Data with Different Units.
- 4) - Converting Units for Derived Quantities.
- 5) - Complementary and Supplementary Angles.
Grade Prefixes:
E: no credit earned toward degree and grade not calculated in GPA, (Elementary Algebra 025, Intermediate Algebra 026, etc.)
How can I get good at algebra fast? ›
The best way to improve your algebra skills is to practice regularly and learn from your mistakes. You can practice by doing exercises, quizzes, puzzles, or games that involve algebra. You can also use online tools, apps, or websites that offer interactive algebra lessons, tutorials, or feedback.
What does intermediate mean in algebra? ›
An intermediate-level study of algebra involves familiarity with introductory topics to a high level and a multitude of new topics.
Answer/Discussion to 1a 
and
is not a perfect square, it does have a factor that we can take the square root of. 
is
