Reviewing Algebra for CAT6 Test: 3 Challenging Problems

In summary, the speaker is reviewing their algebra textbook for a test and has encountered three difficult problems. The first problem involves roots and the speaker's answer was (36x^3)^(1/2), while the book's answer is (6x)^(5/2). The second root problem involves fractions and the speaker's answer is x^(3/4), while the book's answer is x^(11/4). The last problem is about factoring and the speaker made a mistake by pulling out a factor of (x+16) when simplifying the expression. They also mention using the distributive property and making a mistake with like terms. They express a preference for calculating roots exponentially rather than using a radical.
  • #1
Imparcticle
573
4
I am currently reviewing my whole algebra textbook for a CAT6 test on tuesday. Apparently, it is very difficult, so I'm taking every minute to review.
Anywho, I ran into 3 problems that are currently driving me crazy. :tongue:

One concerns roots.
Here is the problem the book presents:
(6x2x)x1/2

My answer was (36x3)1/2. But the book says the answer is (6x)5/2

BTW, how do you write root signs using the latex program?

another root problem:

y3/y1/4

My answer was x3/4. The book says x11/4 is the answer.

Now, here is a factoring problem:
-4(x+16)4 + 9(x+16)2 + x + 16

On this problem, the part that confuses me is the answer:
[-4(x+16)3 + 9x + 145) (x+16)

I arrived at this answer on my own, except I went one step further:
when I got to [-4(x+16)3 + 9x + 145) (x+16) , I went ahead and rewrote (x+16)3 as (x+16)(x+16)2 so that I could distribute the -4. I then arrived at (x+16)3 (5x+81). Apparently, my final step was incorrect. I would like to know why.

Also, I did most of these operations in my head (as it is easier for me to do so), so if you would like me to explain anything that I did, I should point out that I may sound unmathematical in a sense.

Thank you for your time.
 
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  • #2
The book is wrong on the first problem, and so are you. ;) Remember the rule that says [tex]a^xa^y = a^{x + y}[/tex]. This rule works even when x or y are fractions.

[tex](6x^2x)x^{1/2} = (6x^3)x^{1/2} = 6x^3x^{1/2} = 6x^{3 + 1/2} = 6x^{7/2}[/tex]

For the second problem, remember [tex]\frac{a^x}{a^y} = a^{x - y}[/tex], even when x or y are fractions.

[tex]\frac{y^3}{y^{1/4}} = y^{3 - 1/4} = y^{11/4}[/tex]
 
  • #3
And the last part on factorization. It's just wrong. You cannot pull a factor of x+16 out of the expression again after you've simplified it once. What do you mean to do in "distributing the -4"? You have done something that is against the laws of arithmetic and algebra, that's all.
 
  • #4
Muzza: Thank you for your kind explanation. It seems to me that from now on, it is far more efficient to calculate roots exponentially; without using a radical.

Mattgrime: When I said "distribute the -4", I meant applying the distributive property.

But I see the mistake now. They weren't like terms? (I am referring to the factoring problem)
 

1. What is the purpose of reviewing algebra for the CAT6 test?

Reviewing algebra for the CAT6 test helps students to refresh their knowledge and skills in this subject, which is a crucial component of the test. It allows them to familiarize themselves with the types of questions they can expect and build confidence in their abilities to solve challenging problems.

2. How can I effectively review algebra for the CAT6 test?

To effectively review algebra for the CAT6 test, it is important to start early and practice consistently. Use resources such as textbooks, practice tests, and online tutorials to review key concepts and solve problems. Make sure to also focus on areas where you struggle and seek help from a teacher or tutor if needed.

3. Are there any specific areas of algebra that I should focus on for the CAT6 test?

Yes, there are certain areas of algebra that are commonly tested on the CAT6 test. These include solving linear equations, working with exponents and radicals, and graphing linear and quadratic equations. It is important to review these topics thoroughly and practice solving problems in these areas.

4. How can I approach solving challenging algebra problems on the CAT6 test?

When faced with challenging algebra problems on the CAT6 test, it is important to read the question carefully and identify the key information given. Use strategies such as plugging in numbers, working backwards, and eliminating answer choices to help you solve the problem. Practice using these strategies during your review to build confidence in your problem-solving abilities.

5. How many algebra problems can I expect on the CAT6 test?

The number of algebra problems on the CAT6 test can vary, but typically there are about 10-15 questions in this subject area. It is important to review and practice a variety of problems to prepare for different types of questions that may appear on the test.

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