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Thank you, Bob. Let me see if I can delete the most recent post and start fresh new.
Are you following me? I thank you for your input.
Thanks for the practice problems. I will explore each in greater detail on my days off.
Really? I didn't know this fact. Math is a great road of information.
Thank you, Bob.
Calculators do it all today but calculators also hinder the learning process to some degree. Do you agree?
Scientific notation helps scientists to read and write big and small numbers in a unique, to the point way.
Yes? No?
P. S. We will stick to one topic at a time. It does make sense for me to post many questions representing various math topics.
You subtracted one fraction from another to show that the result will always be
rational.
Let me see.
(1/2) - (1/4) = 1/4
We know that 1/4 is a rational number.
Bob,
I see that you are the only member answering my questions. Is there anyone else who can help you? It just doesn't seem right for one person to do all the math work. I do show effort when the question is not over my head.
Bob,
Thank you for the link. I don't have a computer or laptop.
Can I upload pictures using my android phone? I will try to upload one or two photos following the steps provided in the link.
I thought the decimal point moves the number of spaces indicated by the power of 10.
Yes? No?
Are you saying that the sqrt{ x^(2) } = -x or x?
To assure a positive x, we place the variable x inside absolute value bars.
Yes?
Understood. Thanks.
Bob,
You are right. I apologize for posting so many questions all at once. I will do as you say. I will post one problem at a time and wait for a reply to continue our discussion. Sometimes, I get overly excited when it comes to math.
So, when we take the square root there are always two answers:
A. Positive
B. Negative
The P.S.R. represents the positive answer.
P.S.R = PRINCIPAL SQUARE ROOT
so, sqrt{81} = -9 and 9.
The P.S.R. answer is 9, that is, positive 9.
College Algebra
Section R.2
Please explain, in your own words, the definition of the principal square root.
Sullivan stated the following definition on page 23.
If a is a nonnegative real number, the nonnegative number b such that b^(2) = a
is the principal square root of a, and is denoted by b = sqrt{ a }.
The definition is not too clear.
College Algebra
Section R.2
A. Why is the principal square root of 0 is 0?
Why not the absolute value of 0?
B. If c is greater than or equal to 0, then (sqrt{ c })^2 = c.
Why is the answer c and not the absolute value of c?
College Algebra
Section R.2
Write each number as a decimal.
A. 2.1 x 10^(4)
Answer: 21,000
To obtain the answer, I moved the decimal point 4 places to the right.
Why move the decimal point to the right?
B. 3.26 x 10^(-5)
Answer: 0.0000326
To obtain the answer, I moved the decimal point 5 places to the left.
Why move the decimal point to the left?
College Algebra
Section R.2
Write each number in scientific notation.
A. 9582
Answer: 9.582 x 10^(3)
To obtain the answer, I moved the decimal point 3 places to the left.
This yielded 9.582. Why is 10 raised to a positive power?
B. 0.285
Answer: 2.85 x 10^(-1)
To obtain the answer, I moved the decimal point one place to the right.
This yielded 2.85. Why is 10 raised to a negative power?
College Algebra
Section R.2
Michael Sullivan introduces the idea of square roots on page 24.
According to Sullivan:
sqrt{ a^2 } = | a |, where "a" is any real number.
Sample:
sqrt{ x^2 } = | x |.
Why is the answer the absolute value of x and not simple x?
Can you recommend a good math site or YouTube video clip that goes a little deeper into the realm of real numbers?
I learn via examples. Can you provide a simple example for me to use as study notes?
Can you show me what you mean?
A great, simple reply. Thank you, Bob. Can you please type the steps needed for me to upload math photos here? Why not program the site to have a more up-to-date method for uploading photos, which is so important for students? The geometric interpretation helps out a great deal.
College Algebra
Section R.1
Both (a/0), where a does not equal 0 and 0/0 are undefined, but for different reasons. In your own words explain the different reasons.
College Algebra
Section R.1
Why is the sum of a rational and irrational number irrational?
College Algebra
Section R.1
Are there any real numbers that are neither rational or irrational?