初中数学题库八年级6.5：运用完全平方公式和提取公因式化简二次根式例题解析
原式\(\displaystyle =\left[ {\sqrt{5}+\left( {\sqrt{3}-\sqrt{2}} \right)} \right]\left[ {\sqrt{5}-\left( {\sqrt{3}-\sqrt{2}} \right)} \right]\left[ {\left( {\sqrt{2}+\sqrt{3}} \right)-\sqrt{5}} \right]\left[ {\left( {\sqrt{2}+\sqrt{3}} \right)+\sqrt{5}} \right]\)
\(\displaystyle =\left[ {5-\left( {3+2-2\sqrt{6}} \right)} \right]\left[ {\left( {2+3+2\sqrt{6}} \right)-5} \right]\)
\(\displaystyle =2\sqrt{6}\times 2\sqrt{6}\)
\(\displaystyle =24\)
原式\(\displaystyle =\left[ {{{{\left( {2\sqrt{3}-\sqrt{{11}}} \right)}}^{{16}}}{{{\left( {2\sqrt{3}+\sqrt{{11}}} \right)}}^{{16}}}} \right]\left( {2\sqrt{3}+\sqrt{{11}}} \right)\)
\(\displaystyle ={{\left[ {\left( {2\sqrt{3}-\sqrt{{11}}} \right)\left( {2\sqrt{3}+\sqrt{{11}}} \right)} \right]}^{{16}}}\left( {2\sqrt{3}+\sqrt{{11}}} \right)\)
\(\displaystyle ={{1}^{{16}}}\left( {2\sqrt{3}+\sqrt{{11}}} \right)\)
\(\displaystyle =2\sqrt{3}+\sqrt{{11}}\)
原式\(\displaystyle =\sqrt{{15}}\times \sqrt{5}-2\sqrt{{10}}\times \sqrt{5}+\sqrt{{30}}\times \sqrt{5}\) ------------运用乘法分配律
\(\displaystyle =\sqrt{{75}}-2\sqrt{{50}}+5\sqrt{6}\)
\(\displaystyle =5\sqrt{3}-10\sqrt{2}+5\sqrt{6}\)
