Mrfootballman97
How do you simplify:
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Mrfootballman97
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\[\sqrt{72} \]
KonradZuse
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Okay so some easy steps to start simplifying.
KonradZuse
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First you're going to want to try to split that 72 into something you know can factor.
KonradZuse
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Any idea what 72 can be split into?
Mrfootballman97
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36?
KonradZuse
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and what?
Mrfootballman97
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ohhhhh. Do you mean like 8 times 9?
KonradZuse
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yes, or like tyou said 36 times what? Your first guess was correct.
Mrfootballman97
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so then what?
Mrfootballman97
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or is that the answer? lol
KonradZuse
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\[\sqrt{36 * ?}\]
KonradZuse
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\[\sqrt{36 * 2}\]
KonradZuse
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now can you simplify sqrt(36 or sqrt(2)?
KonradZuse
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WE don't split it up, so sorry if that last comment is confusing....
KonradZuse
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WE can just look at each piece now, and determine what's needed....
abb0t
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You can also use 8 and 9...
KonradZuse
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yes, we can abb0t.... but this is easier. I was going to show 8 and 9 after.
Mrfootballman97
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i can simplify 36 into
Mrfootballman97
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\[\sqrt{6 * 6}\]
KonradZuse
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nono, we don't need to simplify it that way. I meant does sqrt(36) or sqrt(2)= anything?
Mrfootballman97
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oh yeah, 36= 6 and 2= 1.414214562. do i have to simplify 2?
KonradZuse
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correct so we get \[6 \sqrt{2}\] which is our answer.
Mrfootballman97
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ahhhhhhh thanks a lot
KonradZuse
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we don't need to simplify 2, we just need to get it into it's simpliest form.
KonradZuse
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so for example, lets use 8 and 9.
KonradZuse
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\[\sqrt{72} = \sqrt{8 * 9} = 3 \sqrt{ 4 * 2} = 2 *3 \sqrt{2} = 6 \sqrt{2}\]
KonradZuse
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Its' really just trying to take some ugly sqrt thart we cannot solve and split it into things that we can solve for :).
Mrfootballman97
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i liked the 36 and 2 one better lol. Thanks again!
KonradZuse
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Yeah, it's easier, but you can see how it can be applied with any set :). Good luck, I hope you understand the concepts.
Mrfootballman97
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so lets see if i have this:
KonradZuse
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Sure, throw up a random # and lets see if we can solve.
KonradZuse
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as long as it's not prime... AHAH..
Mrfootballman97
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\[\sqrt{75} = 5\sqrt{3}\]
KonradZuse
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yes.
Mrfootballman97
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yaaahooooo
Mrfootballman97
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ok thanks cya later!
KonradZuse
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\[\sqrt{75} = \sqrt{25 * 3} = 5 \sqrt{3}\]
KonradZuse
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np good luck.
Mrfootballman97
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Hey here is a new type of problem:
Mrfootballman97
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\[\sqrt{5} \times \sqrt{35}\]
Mrfootballman97
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Think you can do that?
KonradZuse
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hmm Idk man you're asking a lot here... :p
KonradZuse
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lets start off basic. Multiply them together, what do we get?
KonradZuse
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or, if you want, you can split sqrt(35) into 2 parts, and go that way :).
Mrfootballman97
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well i dont need to get the answer to the equation, i think i just need to simplify it. Its under the section of simplifying
Mrfootballman97
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so do i just simplify each part?
KonradZuse
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simplifying is the same thing.
KonradZuse
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you basically are given an eq, to solve. IT could be multiplication, addition, etc, etc. Then you want to use the elements to combine and form something you are able to simplify and take something out of the sqrt. That is our main objective, to get a real number.
KonradZuse
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We are doing exactly what we did before, exept we are adding an additional step. Instead of 35 and 5, we had 36 and 2. or 9 and 8(9 * 4 *2)
KonradZuse
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I guess above I shouldn't have said you shouldn't split them out, because in the end you can, and it doesn't matter.... sqrt(36) * sqrt(2) is the same thing
KonradZuse
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6 * sqrt(2)
Mrfootballman97
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so would it be sqrt(5) and 35= 7 * 5
Mrfootballman97
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\[\sqrt{5} \times \sqrt{7} \times \sqrt{5}\]?
Mrfootballman97
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but those are primes....
KonradZuse
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yessir, but you can combine them in other ways, no?
KonradZuse
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sqrt(5) * sqrt(5) = ?
Mrfootballman97
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i dont know. So then what do i do?
Mrfootballman97
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oh didnt see your comment
KonradZuse
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Always remember when we have 2 of the same sqrt() we get the actual number
Mrfootballman97
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25?
Mrfootballman97
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oops 5
KonradZuse
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sqrt(25)yes.
KonradZuse
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and yes.
Mrfootballman97
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wait...
KonradZuse
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we now have our answer.
Mrfootballman97
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so how do i write down this answer?
KonradZuse
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5sqrt(7)
Mrfootballman97
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ohhhh ok
KonradZuse
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Math is awesome that you can combine and move things around to find whatever you need.
Lets say we have sqrt(3) sqrt(3) and sqrt(4) the 2 sqrt(3) become a 3. and the sqrt(4) becomes a 2. Our answer is 6.
KonradZuse
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But if we had lets say sq(15) and sqrt(3) we will have to split up the sqrt(15) into sqrt(3) sqrt(5) and then another sqrt(3) which we end up getting 3sqrt(5)
Mrfootballman97
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ahhhhhhhh that makes sense! Are you a math teacher or something?
KonradZuse
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haha na...
KonradZuse
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I just know how much it sucks to not get proper help.....
Mrfootballman97
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yeah man. Ok well you saved my grade! Thanks again
KonradZuse
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No problem good luck ,anymore questions you can do @konradzuse to get me.
Mrfootballman97
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ok lets hope i dont need to do that :P
KonradZuse
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There are lots more math in your future :).
Mrfootballman97
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true that.
KonradZuse
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:) I just got done with Linear Algebra and Calculus 2 :)
Mrfootballman97
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im half way through geometry...
Mrfootballman97
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hey would the answer to sqrt of 9 over 5 = sqrt of 45 over 5?
Mrfootballman97
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|dw:1358109390649:dw|
Mrfootballman97
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@KonradZuse
KonradZuse
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nope... what's sqrt(9)?
Mrfootballman97
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would it be:
Mrfootballman97
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\[\sqrt{3\sqrt{5}}\]
KonradZuse
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nope 3/sqrt(5)...
Mrfootballman97
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ohh
Mrfootballman97
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so just:
Mrfootballman97
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|dw:1358110687298:dw|
Mrfootballman97
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or should it have a sqrt sign over the entire thing?
KonradZuse
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think about it.
sqrt(9)/sqrt(5) is the same thing as sqrt(9/5) sqrt(9) is 3.
Mrfootballman97
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ok thanks. Have a good day
KonradZuse
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yup.
KonradZuse
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you can also double check everything with a calculator...