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第98页

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$解：原式 ={\sqrt {4{x}^{2}(3y+6{y}^{3})}}$

$={\sqrt {4{x}^{2}}}·{\sqrt {3y+6{y}^{3}}}$

$=2x{\sqrt {3y+6{y}^{3}}}$

$={({\sqrt {3}}×{\sqrt {5}})}×({\sqrt {5}}×{\sqrt {7}})$

$=({\sqrt {5}×{\sqrt {5}}})×({\sqrt {3}×{\sqrt {7}}})$

$=5{\sqrt {21}}$

$=({\sqrt {3}×{\sqrt {6}}})×2{\sqrt {6}}$

$={\sqrt {3}×({\sqrt {6}}}×2{\sqrt {6}})$

$=12{\sqrt {3}}$

$={\sqrt {56×{\frac {1} {7}}}}$

$={\sqrt {8}}$

$=2{\sqrt {2}}$

$={\sqrt {54×{\frac {2} {3}}}}$

$={\sqrt {36}}$

$=6$

$={\sqrt {\frac {a} {2}·4{a}^{2}}}$

$={\sqrt {2{a}^{3}}}$

$=a{\sqrt {2a}}$

$={\sqrt {{a·a}^{3}{b}^{2}}}$

$={\sqrt {{a}^{4}{b}^{2}}}$

$={a}^{2}b$

$解：{\sqrt {{10}^{2}+{20}^{2}}}=10{\sqrt {5}}(cm)$

$答：斜边的长为10\sqrt {5}cm。$