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April 22nd, 2016, 09:07 AM   #1
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need some explanation about square roots

I know about roots and the quadratic formula, but I need some explanation about what was done here


from the part where the square root of 8 became the square roots of 4 and 2 to the end of this, especially the third line.

Last edited by skipjack; April 22nd, 2016 at 07:47 PM.
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April 22nd, 2016, 09:27 AM   #2
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You may want to do some additional exercises on surds. It's important to have a good background in the arithmetic of surds before getting to quadratic equations.

Mainly, the second line was about simplifying the part in the square root. 8 is made up of three factors 2 x 2 x 2, and you know that 2 x 2 is a square, so you can find the square root of 2 x 2 (i.e. 2) and move it outside the square root sign. $\displaystyle \sqrt 8 = \sqrt{4 \times 2} = \sqrt 4 \sqrt 2 = 2 \sqrt 2$.

The remaining steps were about fraction reduction, the same way you'd reduce a fraction from, say, $\displaystyle \displaystyle{2 \over 4}$ to $\displaystyle \displaystyle{1 \over 2}$.
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April 22nd, 2016, 11:39 AM   #3
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Surely you know that 8= 4*2. And then $\displaystyle \sqrt{2*4}= \sqrt{2}\sqrt{4}$ and $\displaystyle \sqrt{4}= 2$. Putting those together, $\displaystyle \sqrt{8}= \sqrt{4*2}= 2\sqrt{2}$.

Last edited by skipjack; April 22nd, 2016 at 07:45 PM.
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April 22nd, 2016, 03:12 PM   #4
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Someone should make a macro for countryboy that converts [tex] to [math] when on MMF
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April 22nd, 2016, 07:51 PM   #5
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Quote:
Originally Posted by kate09 View Post
. . . especially the third line.
As "2" is appears in both the numerator and the denominator, it cancels. Did you mean to refer to this line?
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April 23rd, 2016, 01:47 AM   #6
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Quote:
Originally Posted by Joppy View Post
Someone should make a macro for countryboy that converts [tex] to [math] when on MMF
Is he from an SMF-based forum?
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April 23rd, 2016, 02:24 AM   #7
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I don't know of any mathematics forum using SMF.
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April 23rd, 2016, 07:17 AM   #8
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Quote:
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Someone should make a macro for countryboy that converts [tex] to [math] when on MMF
I sent a private message to him about using them. If his posts are edited, and he leaves and never looks back
at them, he probably wouldn't know that his way doesn't work on here.
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May 12th, 2016, 03:48 PM   #9
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I don't know of any mathematics forum using SMF.
A science forum in my country uses SMF, and it uses MimeTeX with codes (though it doesn't work anymore).
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May 14th, 2016, 06:29 AM   #10
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I was worried at first. The last thing I need is yet another math forum to spend time on! Fortunately that one was not in any language I read.
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