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Square root problem

  1. Jun 21, 2015 #1
    Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)?

    Kind regards,
    Christian
     
  2. jcsd
  3. Jun 21, 2015 #2

    pwsnafu

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    Science Advisor

    Well, what do you get when you add a number to itself?
     
  4. Jun 21, 2015 #3

    Mentallic

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    Homework Helper

    These rules apply:

    [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

    [tex]ab+ac=a(b+c)[/tex]
     
  5. Jun 21, 2015 #4
    Ohh of course! thank you very much :)
    So it's

    sqrt(10^2 +10^2) = sqrt(2*10^2) = sqrt(10^2)*sqrt(2)= 10*sqrt(2).
     
  6. Nov 15, 2016 #5
    ##\sqrt{10^2+10^2}##

    ##\sqrt{a^2+a^2}=\sqrt{2a^2}##

    Similarly

    ##\sqrt{10^2+10^2}=\sqrt{2(10)^2}##

    ##\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}##

    Similarly
    ##=\sqrt{2(10)^2}=\sqrt{2}\cdot\sqrt{10^2}##

    ##=10\sqrt{2}##
     
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