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Thinking Mathematically

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　1.{\McS\char 108}{\McS\char 18} $3\sqrt{2}$ + $5\sqrt{2}$ - $4\sqrt{2}$ =

　2.{\McS\char 108}{\McS\char 18} $2\sqrt{3}$ + $3\sqrt{5}$ - $6\sqrt{3}$ =

　3.{\McS\char 108}{\McS\char 18} $3\sqrt{2}$ $\times$ $5\sqrt{2}$ =

　4.{\McS\char 108}{\McS\char 18} $3\sqrt{2}$ $\times$ $3\sqrt{5}$ =

　5.{\McS\char 108}{\McS\char 18} $\sqrt{12}$ $\div$ $\sqrt{2}$ =

　6.{\McS\char 108}{\McS\char 18} $\sqrt{20}$ $\div$ $\sqrt{5}$ =

　7.{\McS\char 108}{\McS\char 18} $\frac{\sqrt{28}}{\sqrt{6}}$ =

　8.{\McS\char 108}{\McS\char 18} $\frac{\sqrt{60}}{\sqrt{8}}$ =

 

$\spadesuit${\MbS\char 48}{\MbS\char 151}{\MaS\char 231}{\McS\char 51}{\MbS\char 19}{\MbS\char 106}{\MgS\char 59}{\MaS\char 139}{\MbS\char 193}{\MbS\char 182}

 

　 {\MaS\char 202}{\McS\char 170}{\McS\char 87}{\McS\char 251}{\MaS\char 134}{\McS\char 171}{\McS\char 18}{\MaS\char 53}{\MaS\char 135}, {\MbS\char 98}{\MaS\char 231}{\MbS\char 217}{\MaS\char 228}{\MfS\char 122}「{\MgS\char 59}{\McS\char 85}」{\MbS\char 170}{\MdS\char 245}{\MaS\char 224}{\MaS\char 45}:

{\MaS\char 248}$\sqrt{2}${\MbS\char 245}{\MbS\char 65}{\MbS\char 117}{\McS\char 248}{\MaS\char 95}{\MdS\char 202} {\MaS\char 3}2{\MaS\char 4} {\MbS\char 237}{\MhS\char 34}{\MaS\char 65}{\MaS\char 1}{\MhS\char 34}{\MaS\char 55}{\MiS\char 2}, {\MdS\char 135}2{\MbS\char 20}{\MfS\char 17}{\MdS\char 134}, {\McS\char 201}{\MaS\char 202}{\MhS\char 97}{\MhS\char 27}{\MaS\char 50}

{\MaS\char 176}{\MbS\char 220}$\sqrt{5}${\MbS\char 245}{\MbS\char 65}{\MbS\char 117}{\McS\char 248}{\MaS\char 95}{\MdS\char 202} {\MaS\char 3}5{\MaS\char 4} {\MbS\char 237}{\MhS\char 34}{\MaS\char 65}{\MaS\char 1}{\MhS\char 34}{\MaS\char 55}{\MiS\char 2}, {\MdS\char 135}2{\MbS\char 20}{\MfS\char 17}{\MdS\char 134}, {\McS\char 201}{\MaS\char 202}{\MhS\char 97}{\MhS\char 27}{\MaS\char 50}

{\MbS\char 70}{\MaS\char 74}$3\sqrt{2}$ + $5\sqrt{2}$ {\MbS\char 60}{\MbS\char 50}{\MaS\char 255}{\MbS\char 117} = {\MaS\char 114}{\McS\char 182}{\MbS\char 127}8{\MaS\char 95}{\MdS\char 135}2{\MbS\char 20}{\MfS\char 17}{\MdS\char 134}, {\MdS\char 202} {\MaS\char 3}2{\MaS\char 4} {\MbS\char 237}{\MhS\char 34}{\MaS\char 65}{\MaS\char 1}

{\McS\char 181}{\McS\char 243} $2\sqrt{3}$ + $3\sqrt{5}${\MaS\char 162}{\MbS\char 117}{\MaS\char 66}{\McS\char 243}{\MbS\char 60}{\MbS\char 50}{\MdS\char 225}?

　 {\MfS\char 119}{\MaS\char 44}{\McS\char 122}{\MbS\char 112}, {\McS\char 91}{\MbS\char 253}{\MbS\char 127}2{\MaS\char 95}{\MdS\char 135}2{\MbS\char 20}{\MfS\char 17}{\MdS\char 134}, {\MdS\char 202} {\MaS\char 3}3{\MaS\char 4} {\MbS\char 237}{\MhS\char 34}{\MaS\char 65}{\MaS\char 184}3{\MaS\char 95}{\MdS\char 135}2{\MbS\char 20}{\MfS\char 17}{\MdS\char 134}, {\MdS\char 202}

{\MaS\char 3}5{\MaS\char 4}{\MbS\char 237}{\MhS\char 34}{\MaS\char 65}, {\MaS\char 196}{\MbS\char 209}{\MaS\char 70}{\MaS\char 98}{\MbS\char 237}{\MaS\char 177}{\MaS\char 229}{\MbS\char 117}{\MaS\char 46}{\MaS\char 176}{\MbS\char 237}, {\McS\char 65}{\MbS\char 205}{\MbS\char 204}{\MbS\char 182}{\MaS\char 139}{\MaS\char 202}{\McS\char 248}{\McS\char 150}{\MaS\char 55} 

{\MaS\char 130}{\MbS\char 224}{\McS\char 165}{\MaS\char 95}{\MbS\char 170}{\MdS\char 245}, {\MbS\char 19}{\MbS\char 106}{\MgS\char 59}{\MbS\char 237}{\MaS\char 139}{\MbS\char 193}{\MbS\char 182}, {\MbS\char 64}{\McS\char 118}{\MaS\char 46}{\MbS\char 117}{\MaS\char 189}{\McS\char 230}{\MaS\char 55}{\MaS\char 1}

$\diamond${\McS\char 42}{\McS\char 51}$\diamond$

 

 

$\diamond${\MbS\char 90}{\McS\char 172}{\McS\char 65}{\MbS\char 104}$\diamond$
$\diamond${\McS\char 42}{\McS\char 51}$\diamond$

　1.{\McS\char 108}{\McS\char 18} $\sqrt{3}$ - $5\sqrt{3}$ - $2\sqrt{3}$ =

　2.{\McS\char 108}{\McS\char 18} $2\sqrt{2}$ + $3\sqrt{5}$ - $6\sqrt{2}$ =

　3.{\McS\char 108}{\McS\char 18} $3\sqrt{5}$ + $\sqrt{5}$ - $4\sqrt{7}$ =

　4.{\McS\char 108}{\McS\char 18} $4\sqrt{2}$ + $3\sqrt{6}$ - $\sqrt{6}$ =

$\spadesuit${\MbS\char 48}{\MbS\char 151}{\MaS\char 231}{\McS\char 51}{\MbS\char 19}{\MbS\char 106}{\MgS\char 59}{\MdS\char 13}{\McS\char 206}{\MbS\char 182}:

　 $\sqrt{2}$ $\times$ $\sqrt{3}$ {\MbS\char 117}{\MaS\char 66}{\McS\char 243}{\MbS\char 60}{\MbS\char 50}{\MdS\char 225}?

{\McS\char 237}{\MaS\char 108},$\sqrt{2}$ {\MaS\char 184} $\sqrt{3}$ {\McS\char 183}{\MbS\char 117}{\MdS\char 135}２{\MbS\char 20}{\MfS\char 17}{\MdS\char 134},

{\MbS\char 109}{\MbS\char 205}{\MdS\char 134}{\MbS\char 130}{\MbS\char 243}{\MaS\char 176}, {\MbS\char 64}{\McS\char 118}{\MaS\char 170}{\MaS\char 74}{\MfS\char 122}{\MaS\char 115}{\MaS\char 95}{\McS\char 201}{\MaS\char 202}{\McS\char 248}{\McS\char 150}{\MdS\char 223}!

　 {\MbS\char 70}{\MaS\char 74},$\sqrt{2}$ $\times$ $\sqrt{3}$ = $\sqrt{2\times3}$ = $\sqrt{6}$

　 {\McS\char 181}{\McS\char 206}{\MbS\char 182}{\MaS\char 162}{\MaS\char 224}{\MaS\char 83}? $\sqrt{12}$ $\div$ $\sqrt{2}$ = ?

{\MaS\char 176}{\MbS\char 154}{\McS\char 173}{\MbS\char 220}, {\MaS\char 196}{\MbS\char 209}{\MdS\char 134}{\MbS\char 130}{\MbS\char 243}{\MaS\char 176}, {\MaS\char 170}{\MaS\char 74}{\MfS\char 122}{\MaS\char 115}{\MaS\char 95}{\McS\char 201}{\MaS\char 202}{\McS\char 248}{\McS\char 150}!

$\sqrt{12}$ $\div$ $\sqrt{2}$ = $\sqrt{12\div2}$ = $\sqrt{6}$

 

 

　1.{\McS\char 108}{\McS\char 18} $\sqrt{3}$ $\times$ $\sqrt{5}$ =

$\diamond${\McS\char 42}{\McS\char 51}$\diamond$

　2.{\McS\char 108}{\McS\char 18} $4\sqrt{6}$ $\times$ $3\sqrt{2}$ =

　3.{\McS\char 108}{\McS\char 18} $2\sqrt{3}$ $\div$ $3\sqrt{5}$ =

　4.{\McS\char 108}{\McS\char 18} $12\sqrt{6}$ $\div$ $4\sqrt{2}$ =

　

 

　1.{\MbS\char 243}{\MaS\char 176} {\MaS\char 3}{\MdS\char 134}{\MbS\char 130}{\MaS\char 4}({\MdS\char 185}{\MbS\char 243}{\MaS\char 176}{\MbS\char 159}{\MbS\char 106}{\MbS\char 237}{\MgS\char 59}{\McS\char 85}) {\MaS\char 47}{\MaS\char 176}{\McS\char 248}{\MaS\char 95} {\MaS\char 3}{\MaS\char 65}{\MaS\char 4}({\MbS\char 98}{\MaS\char 229}), 才{\MaS\char 170}{\MbS\char 243}

　　{\MaS\char 139}{\MbS\char 193}{\MaS\char 1}

$\diamond${\McS\char 33}{\McS\char 127}$\diamond$
$\diamond${\MbS\char 98}{\MaS\char 231}{\MbS\char 217}{\MaS\char 228}{\MbS\char 237}{\McS\char 122}{\MbS\char 112}$\diamond$

　2.{\MaS\char 176}{\MbS\char 154} {\MaS\char 3}{\MdS\char 134}{\MbS\char 130}{\MaS\char 4}({\MdS\char 185}{\MbS\char 243}{\MaS\char 176}{\MbS\char 159}{\MbS\char 106}{\MbS\char 237}{\MgS\char 59}{\McS\char 85}), {\MaS\char 79}{\MaS\char 46}{\McS\char 248}{\MaS\char 236}{\McS\char 98}{\MaS\char 176}{\McS\char 248}{\MaS\char 95} {\MaS\char 3}{\MaS\char 65}{\MaS\char 4}({\MbS\char 98}{\MaS\char 229}

　　), {\MaS\char 255}{\MaS\char 170} {\MaS\char 74}{\MbS\char 243}{\MdS\char 13}{\McS\char 206}{\MaS\char 1}

 

 

{\MdS\char 65}{\McS\char 117}{\McS\char 122},{\MaS\char 3}{\MbS\char 248}{\MjS\char 152}{\McS\char 63}{\MbS\char 90}, {\MaS\char 190}{\MiS\char 108}{\MaS\char 215}{\MgS\char 252}{\MaS\char 4}, {\MbS\char 70}{\MaS\char 74}, {\McS\char 44}{\MbS\char 127}{\MbS\char 128}{\MdS\char 134}{\MbS\char 130}{\MbS\char 197}{\MbS\char 237}{\MbS\char 118}{\MaS\char 96}{\MdS\char 223}!

{\MaS\char 87}{\MaS\char 224}$\sqrt{4}${\MbS\char 128}{\MdS\char 134}{\MbS\char 130}{\MbS\char 197}{\MaS\char 55}{\MdS\char 253} ? {\MaS\char 196}{\MbS\char 209},$4=2^2$, {\MbS\char 70}{\MaS\char 74} $\sqrt{4} = \sqrt{2^2}$,

{\McS\char 165}{\McS\char 91}{\MbS\char 253} {\MaS\char 3}2{\MaS\char 4} {\McS\char 165}{\MaS\char 95}{\MhS\char 34}{\MaS\char 65}{\MbS\char 11}{\MeS\char 17}{\MhS\char 27}{\MbS\char 20}, {\MaS\char 170}{\MaS\char 74}{\MaS\char 124}{\MhS\char 42}{\MaS\char 55} {\MaS\char 1}

{\MaS\char 196}{\MbS\char 164} $\sqrt{4} = \sqrt{2^2} = 2$

 

 

　1.{\McS\char 108}{\McS\char 18} $\sqrt{36}$ =

　2.{\McS\char 108}{\McS\char 18} $\sqrt{81}$ =

　3.{\McS\char 108}{\McS\char 18} $\frac{\sqrt{25}}{\sqrt{49}}$=

　4.{\McS\char 108}{\McS\char 18} $\sqrt{1\frac{11}{25}}$ =

 

　　

　1.{\McS\char 165}{\MhS\char 185}{\MbS\char 100}{\McS\char 14}{\MbS\char 237}{\MbS\char 241}{\MbS\char 237}, {\MbS\char 117}{\MaS\char 202}{\McS\char 122}{\MbS\char 112}{\MaS\char 224}{\MaS\char 83}{\MaS\char 248}{\MbS\char 106}{\MgS\char 59}{\MbS\char 127}{\MjS\char 24}{\MaS\char 147}{\MaS\char 1}{\MiS\char 233}{\MaS\char 231}{\MbS\char 222}{\MaS\char 241}{\MbS\char 113}{\MbS\char 81}{\MaS\char 167}{\MbS\char 106}

　　{\MgS\char 59}{\McS\char 108}{\McS\char 18}, {\MbS\char 127}{\McS\char 201}{\MbS\char 98}{\MaS\char 231}{\MgS\char 176}{\McS\char 50}{\McS\char 182}{\MaS\char 77}, {\MaS\char 46}{\MbS\char 117}{\MbS\char 133}{\MbS\char 100}{\McS\char 189}{\McS\char 245}{\MaS\char 1}

　2.{\MdS\char 199}{\MaS\char 213}, {\MbS\char 127}{\McS\char 201}{\MbS\char 107}{\MbS\char 106}{\MgS\char 59}{\MbS\char 237} {\MaS\char 3}{\MbS\char 124}{\McS\char 21}{\MaS\char 4},{\MaS\char 3}{\MbS\char 127}{\MbS\char 220}{\MaS\char 147}{\McS\char 182}{\MaS\char 77}{\MaS\char 4}, {\MbS\char 133}{\MbS\char 100}{\MaS\char 63}{\MbS\char 204}{\MbS\char 84}{\MaS\char 163}, {\McS\char 52}{\MbS\char 15}{\MaS\char 170}{\MjS\char 95}

　　 {\MbS\char 118}{\MbS\char 84}{\MaS\char 88}{\MbS\char 243}{\McS\char 201}{\MaS\char 84}{\MbS\char 182}{\McS\char 68}{\MbS\char 248}{\McS\char 133}, {\McS\char 165}{\MbS\char 154}{\MaS\char 231}{\MbS\char 222}{\MfS\char 110}{\MbS\char 125}{\MiS\char 162}{\MbS\char 125}{\MiS\char 248}{\McS\char 166}{\MaS\char 1}



1999-11-13
11/13/1999		 親愛的，我把根號變成人了~(Cwtex版)

1.方根的計算，有時候是枯燥乏味的，這篇文章嘗試讓方根「擬

　人化」，或許「學數學」會是一種全新的經驗。

2.本文是由「Cwtex」軟體轉檔而成，因此，檔案頗大，請見諒

，這是數學王子的實驗作品。請見「數學文章怎麼排版?」

二、過程說明
數學王子

一、前言

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