Sum of Four Squares and Division
================================
Another one from YouTube I want to solve and I can do it in plain text.
This time, I have the following exercise, and no calculators are allowed:


  60²+61²+62²+63²
  ---------------
        94

And my way to square a two-digit number will be:

  (10a+b)²=100a²+20ab+b²=10a(10a+2b)+b²

Where a and b are digits.

And also,

  94=2✕47

Let's start

      60²+61²+62²+63²
      --------------- =
            94

      60✕60+60✕62+1+60✕64+4+60✕66+9
      ----------------------------- =
                 2✕47

      60✕60+60✕62+60✕64+60✕66+1+4+9
      ----------------------------- =
                 2✕47

      60(60+62+64+66)+14
      ------------------ =
             2✕47

      30(60+62+64+66)+7
      ----------------- =
             47

      30(60+60+2+60+4+60+6)+7
      ----------------------- =
                47

      30(60+60+60+60+12)+7
      -------------------- =
               47

      30(240+12)+7
      ------------ =
           47

      30✕240+360+7
      ------------ =
           47

      30(100+140)+360+7
      ----------------- =
             47


      3000+4200+360+7
      --------------- =
            47

      3000+1000+3200+360+7
      -------------------- =
               47


      4000+3200+360+7
      --------------- =
             47

      4000+700+2500+360+7
      ------------------- =
              47

      4700+2500+360+7
      --------------- =
            47


      4700+50²+360+7
      -------------- =
            47

      4700+50✕50+360+7
      ---------------- =
            47

      4700+50(47+3)+360+7
      ------------------- =
              47

      4700+50✕47+150+360+7
      -------------------- =
              47


      4700+50✕47+150+320+40+7
      ----------------------- =
                  47


      4700+50✕47+470+47
      ----------------- =
             47


      4700+50✕47+10✕47+47
      ------------------- =
              47


      4700+60✕47+47
      ------------- =
           47


      100✕47+60✕47+1✕47
      ----------------- =
             47


      47(100+60+1)
      ------------ =
           47


      100+60+1=161

Awesome!