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math
i'm reviewing for a BIG test i have in math class tomorrow and i can't for the life of me figure out how to do these two problems.
square root of 12. i know the answer is "2 root 3" but i don't remember how you get that.
and when you are using the quadratic formula. the "B squared + or - the square root of B squared + 4 x A x C. all over 2a." if you don't know the quadratic formula then don't answer this. but i substituted the numbers into the formula correctly but i got a negative under the square root and i don't remeber how to simplify it now.
thanks so much!! the test is tomorrow 8[
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Well, under the radical you make the one number two numbers, and hopefully one is a perfect square. For 12, it would be 4 x 3. You can then take out the 4 and by doing that you square root it. That gives you 2 root 3.
The quadratic formula is , -B + or - the square root of b squared minus 4 AC all over 2A (as sung to pop goes the weasel).
If you have a negative under the radical sign, just do it as you normall would, and stick a lowercase i after it. i is the square root of negative one, and it is imaginary.
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umm well 2 root 3 is the square root of 12 because 4x3=12.. 2 is a square root of 4 right? but theres no square root of 3 soo you pull out the 2 and are left w/ 2 root 3.
and yeah to simplify a negative you just act as if it wasnt negative, then square root what you got as you normally would, and put an 'i' after your answer. like if you got negative 12 under your square root then your final answer would be 2i root 3.
haha hope that all made sense. good luck!
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it looks like you have enough help on simplifying radicals (square roots) So I'll help you with the quadratic formula.
If you come up with a negative number under your square root sign, it's called an imaginary number. I'm not sure what grade level of math your in, so if this is something you haven't learned, i'm sorry. I'm in a pre-calculus class. Imaginary numbers are labeled with an "i" For example::
If you get the square root of -16, it would simplify down to "4i" You would just take the square root of 16 as normal but instead of it just being 4, it would be imaginary 4, noted as "4i"
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For the square root thing, it's because 3 x 3 is 6. multiply that by 2 and you get 12. 12 is not a square number though, which is why it's like that. Haha, sorry if my memory is bad though! But that's what I remember :]
edit: okay maybe im wrong, lol. i hate algebra :(
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I don't remember the quadratic formula but to get the square root of 12 you have to simplify it.
The square root of 4 and the square root of 3 give you 12. Then you see that the sqaure root of 4 is a perfect square so that simplifies to 2 and you leave square root of 3 alone because you can't simplify that. So the answer would come out to 2 square root of 3.
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okay, i think i can help. for the square root of 12... okay, you have 12 under the square root sign. then to simplify 12 (still under the square root sign) see if there are any factors of 12 that are perfect squares. what i mean by this is that 4 X 3 = 12, and 4 is a perfect square. this is all still under the square root sign. then, take the square root of 4 (which is 2) and place it outside of the square root sign. then, you have the square root of 3 and you can't simplify that so you have your answer. as for the quadratic formula, you are doing it right, BUT remember how you can't have a negative square root? that means that there is no answer! so the answer would be "undefined" or "none" or whatever. for example, if you have the square root of -16, you can't simplify that because it is impossible to have a negative square root. why is this? 4 X 4 = 16. 4 X 4 will never equal -16, and -4 X -4 will never equal -16. i had this same problem last year because i kept trying to get the square root of negative numbers, but that is impossible. so at that point in the formula, you just write down "undefined" because there is no possible way to simplify it beyond that.
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