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第99頁

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解：原式?$=m(a-b)$?
解： 原式?$=\sqrt {4x^2(2+3x)}$?
?$ =2x\sqrt {3x+2}$?
解：?$(1)\sqrt 3$(答案不唯一)?
?$ (2)6+\sqrt 5$?(答案不唯一)
解：原式?$=\sqrt {(2\sqrt 3)^2-(3\sqrt 2)^2}$?
?$=\sqrt {12+18}$?
?$ =\sqrt {30}$?
解：原式?$=\sqrt {(6\sqrt 5)^2-(-3\sqrt 2)^2}$?
?$=\sqrt {180-18}$?
?$ =\sqrt {162}$?
?$ =9\sqrt 2$?
解：?$(1)AD=6×\frac {\sqrt 3}2=3\sqrt 3(\ \mathrm {cm})$?
?$(2) \mathrm S_{△ABC}=6×3\sqrt 3×\frac 12=9\sqrt 3(\ \mathrm {cm^2})$?
解：?$ (1) \sqrt {5+2 \sqrt 6} $?
?$ =\sqrt {3+2 \sqrt 6+2} $?
?$ =\sqrt {(\sqrt 3)^2+2 ×\sqrt 3 ×\sqrt 2+(\sqrt 2)^2} $?
?$ =\sqrt {(\sqrt 3+\sqrt 2)^2} $?
?$ =\sqrt 3+\sqrt 2 $?

?$(2) $?∵?$\sqrt 3-1>0 $?
∴?$\sqrt {4-\sqrt {12}} $?
?$ =\sqrt {4-2 \sqrt 3} $?
?$ =\sqrt {3-2 \sqrt 3+1} $?
?$ =\sqrt {(\sqrt 3)^2-2 ×\sqrt 3 ×1+1^2} $?
?$ =\sqrt {(\sqrt 3-1)^2} $?
?$ =\sqrt 3-1 $?
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