[MOVED] simplifying square roots: factoring numbers

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Monkeyeatbutt

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Aug 12, 2006
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How do I find the square root of something?

I have to simplify square roots. and the example is as follows:

Code: 
    12
   /  \
  2    6 
      /  \
     2    3 

factors: 2, 2, 3
Then another one next to it that looks like this

Code: 
    12
   /  \
  3    4
      /  \
     2    2

factors: 3, 2, 2
 
If a>0 & b>0 then \(\displaystyle \
\begin{array}{l}
\sqrt {ab} = \sqrt a \sqrt b \\
\sqrt {12} = \sqrt {\left( 4 \right)\left( 3 \right)} = \sqrt 4 \sqrt 3= 2 \sqrt 3 \\
\end{array}\)
ALWAYS look for factors that are perfect squares.
 
What makes a factor a square?

I have no clue why im in a geometry/ trig class (the last half of the class is trig) I never did algebra.
 
Monkeyeatbutt said:
What makes a factor a square?
Click to expand...
A "square" number is a number that is the square of some other number. For instance, 4 is square, because 4 = 2<sup>2</sup>; 9 is square, because 9 = 3<sup>2</sup>; and so forth.

Eliz.
 
Okay; I think I have it: to simplify the square of 96 it would be:

. . .2 square root symbol 48
 
Monkeyeatbutt said:
And to find a factor you mulptly like 5 and 3 are factors of 15 right?
Click to expand...
Factors are the numbers you multiplied to get the number. To find those factors, you divide; customarily, one divides by the smallest prime that one can, working through the primes until the quotient is a prime. For instance:

. . . . .Factor 2100.

. . . . .Since 2100 is even, 2 is a factor:
. . . . .2100 ÷ 2 = 1050

. . . . .Since 1050 is even, 2 is a factor:
. . . . .1050 ÷ 2 = 525

. . . . .Since 525 is not even, 2 is not a factor.
. . . . .Since 5 + 2 + 5 = 12 is divisible by 3, 3 is a factor:
. . . . .525 ÷ 3 = 175

. . . . .Since 1 + 7 + 5 = 13 is not divisible by 3,
. . . . .3 is not a factor.
. . . . .Since 175 ends in 5, 5 is a factor:
. . . . .175 ÷ 5 = 35

. . . . .Since 35 ends in 5, 5 is a factor:
. . . . .35 ÷ 5 = 7

. . . . .Since 7 is itself a prime, we are done.

. . . . .2100 = 7 × 5 × 5 × 3 × 2 × 2

For further information, try doing a search for "factoring", "numbers", "prime", and possible "divisible" or "divisibility tests".

Eliz.
 
Monkeyeatbutt said:
I think I have it: to simplify the square of 96 it would be: 2 square root symbol 48
Click to expand...
Are you working with "the square of 96", namely 96<sup>2</sup>, or with the square root of 96?

How are you getting that 96<sup>2</sup> = 2sqrt[48]?

. . . . .(2sqrt[48])<sup>2</sup> = 4(48) = 192

. . . . .96<sup>2</sup> = 9216

. . . . .sqrt[96] = sqrt[16×6] = sqrt[16]sqrt[6] = 4sqrt[6]

Did you mean any of the above, or did you mean something else?

Thank you.

Eliz.
 
Monkeyeatbutt said:
im in a geometry/ trig class (the last half of the class is trig) I never did algebra.
Click to expand...
HOW IN THE WORLD CAN THAT BE THE CASE?
 
I dont know how I got in this class. I quit highschool but decited to finaly finish it. So im doing on of those home things and for math this is what they gave me. When I was in highschool I did a year of basic math. I have no clue why I got this class.

I dont think i mean any of that stuff. Its kinda hard to explain because I dont have a buttion for the symbol im looking for. Let me try to decribe it all better.

the problem is
simplify: symbol for square root (the check mark thing in PKA's first post) 96

My answer is
2 symbol for square root 48.

thanks for all the help guys Im totaly clueless
 
Monkeyeatbutt said:
I dont know how I got in this class. I quit highschool but decited to finaly finish it. So im doing on of those home things and for math this is what they gave me. When I was in highschool I did a year of basic math. I have no clue why I got this class…. Im totaly clueless
Click to expand...
Well that explains a lot! Thank you.
Now I will give some free advice. Find your self a good website where there are some good tutorials: http://www.Purplemath.com/ or http://www.mathgoodies.com/ to name just two. Go there and do some work in basic pre-algebra and algebra. You are going to be totally frustrated if you do not learn the basics. You will remain totally clueless if you do not do something to correct the problem. There is another way: find a good home schooling website that has a mathematics component. Or see if your state has a chapter of the NTCM that might help you. But do something: It aint going to get any better.
 
If you were placed inappropriately, it might be wise to speak with your academic advisor about corrected placement.

Good luck!

Eliz.
 
I cant change classes. First its $50 to change a class (even if they mess up because by the time yo uknow what your class is yo uusualy have the books) and im paying $2000 for the school and we just bought a house so for the ext few months that $50 is going to fell like $500. Plus Im almost done I have 5 chapters left and Unless i find I have flunked all the tests I dont want to start over agin with another class.

Ive gotten A's in all my other classes and Math is the only class I expect to get lower then a A in so im not to worried about the grade just as long as I pass.

I have looked at alot of web pages trying to figure out whats going on but unless someone is showing me what im doing I have a hard time. Like with some algebra (the first of the book had a little in it) Seeing it on a web page made no sence seeing it in the book made no sence. But someone online helped me work one of my problems step by step and finaly I understood it enough to finish it. I didnt understand it real well but I think I did ok with the rest of that chapter.
 
I just wanted to let you know there's a book called "Algebra 20 minutes a day" by Learning Express. They also make a geometry one. I literally did all 20-odd lessons for 20 minutes and saw major improvement. My algebra skills before SAT and college were basically non-existent due to the high school I went to passed everyone who had sub-par attendance (not literally, but somewhat like that). It took me a month to complete the lessons without cramming. I also picked up a math book by Mark
Dugopolski called "Intermediate Algebra." It consists of algebra 1 and algebra 2 that would prepare you to a transition to Trig. By the way, I only spent $12 for both books.

I know you said that you prefer someone show you how to do the problems to ease you understanding. These are just some possible options if you ever wanted to give them a try. :wink:

I do hope you get some help in math to straighten out any problems you have. It's a wonderful feeling to finally know what you're doing. Sorta like the time I conquered fractions...lol Now I love them in all my problems (with the exception they can take a while to finish)
 
LOL i have no clue what a conquered fraction is but im glad you like it.
lll see if I can find the books next time i go into town (witch should be next week).

But untill then can you guy help me with the square root problem?
 
Monkeyeatbutt said:
...can you guy help me with the square root problem?
Click to expand...
Which one? You've already been provided with detailed explanations of the topic and a complete solution to "Simplify sqrt[96]".

Please clarify the question on which you are needing further assistance, showing how far you have gotten in following the instructions, provided earlier in this thread.

Thank you.

Eliz.
 
Monkeyeatbutt said:
LOL i have no clue what a conquered fraction is but im glad you like it.
Click to expand...

Uhh Letsgetaway meant that he/she has conquered fraction not that he/she likes conquered fraction. There is no such thing as conquered fractions in math.
 
jonboy said:
Monkeyeatbutt said:
LOL i have no clue what a conquered fraction is but im glad you like it.
Click to expand...

Uhh Letsgetaway meant that he/she has conquered fraction not that he/she likes conquered fraction. There is no such thing as conquered fractions in math.
Click to expand...

Yeah. I meant that I learned to do fractions after years of trouble with them. Sorry for confusing you, monkeyeatbutt! :D

Here are some more math links with step-by-step picture & written explanations

http://www.wtamu.edu/academic/anns/mps/math/mathlab/
http://online.math.uh.edu/Math1300/index.html
 
I dont know Im still totaly confused. Maby Im explaing wrong because none of your answers look anything like it does in my book
An example in my book says Simplfy each expression.
Squrt49
Then the answer is
Squrt 49=7 because 7(little2) =49


Ok wate I think I get it and this time I think im right.
The squrt for 96 would be what ever number times its self = 96.

Is that right?

Thanks for the links. Ill check those out
 
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