张灵谱
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例题1、化简：\(\displaystyle \sqrt{{{{{\left( {x+2y} \right)}}^{2}}{{{\left( {x-y} \right)}}^{2}}}},\left( {0<x<y} \right)\)
原式\(\displaystyle =\left| {x+2y} \right|\times \left| {x-y} \right|\)
\(\displaystyle =\left( {x+2y} \right)\left( {y-x} \right)\)
\(\displaystyle =2{{y}^{2}}-2xy+xy-{{x}^{2}}\)
\(\displaystyle =2{{y}^{2}}-xy-{{x}^{2}}\)
例题2、化简：\(\displaystyle \sqrt{{125x{{y}^{2}}{{z}^{3}}\times 25x{{y}^{3}}{{z}^{2}}}}\)
原式\(\displaystyle =\sqrt{{125x{{y}^{2}}{{z}^{3}}}}\times \sqrt{{25x{{y}^{3}}{{z}^{2}}}}\)
\(\displaystyle =5yz\sqrt{{5xz}}\times 5yz\sqrt{{xy}}\)
\(\displaystyle =25xyz\sqrt{{5yz}}\)
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