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April 22nd, 2016, 09:07 AM  #1 
Newbie Joined: Apr 2016 From: outer space Posts: 15 Thanks: 4  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. 
April 22nd, 2016, 09:27 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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 $\displaystyle \displaystyle{1 \over 2}$. 
April 22nd, 2016, 11:39 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
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. 
April 22nd, 2016, 03:12 PM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,798 Thanks: 634 Math Focus: Yet to find out. 
Someone should make a macro for countryboy that converts [tex] to [math] when on MMF 
April 22nd, 2016, 07:51 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,622 Thanks: 2075  
April 23rd, 2016, 01:47 AM  #6 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  
April 23rd, 2016, 02:24 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,622 Thanks: 2075 
I don't know of any mathematics forum using SMF.

April 23rd, 2016, 07:17 AM  #8 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  
May 12th, 2016, 03:48 PM  #9 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  A science forum in my country uses SMF, and it uses MimeTeX with codes (though it doesn't work anymore).

May 14th, 2016, 06:29 AM  #10 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
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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explanation, explenation, roots, square 
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