二次根式測試卷子及答案一、選擇題（每題3分，共30分）1.下列二次根式中，與\(\sqrt{2}\)是同類二次根式的是（）A.\(\sqrt{6}\)B.\(\sqrt{8}\)C.\(\sqrt{12}\)D.\(\sqrt{18}\)2.計算\(\sqrt{48}\)的結果為（）A.\(4\sqrt{3}\)B.\(6\sqrt{3}\)C.\(12\sqrt{3}\)D.\(2\sqrt{3}\)3.若\(\sqrt{a}+\sqrt{b}=0\)，則\(a\)和\(b\)的值分別是（）A.\(a=0,b=0\)B.\(a=0,b\neq0\)C.\(a\neq0,b=0\)D.\(a\neq0,b\neq0\)4.計算\(\sqrt{3}\times\sqrt{6}\)的結果為（）A.\(3\sqrt{2}\)B.\(6\sqrt{3}\)C.\(\sqrt{18}\)D.\(\sqrt{36}\)5.以下哪個表達式等于\(\sqrt{25}\)（）A.\(5\)B.\(-5\)C.\(\pm5\)D.\(\pm\sqrt{5}\)6.計算\(\sqrt{49}\)的結果為（）A.\(7\)B.\(-7\)C.\(\pm7\)D.\(\sqrt{7}\)7.計算\(\sqrt{9}+\sqrt{16}\)的結果為（）A.\(5\)B.\(7\)C.\(9\)D.\(11\)8.若\(\sqrt{a}=3\)，則\(a\)的值是（）A.\(9\)B.\(6\)C.\(3\)D.\(1\)9.計算\(\sqrt{2}\div\sqrt{8}\)的結果為（）A.\(\frac{\sqrt{2}}{4}\)B.\(\frac{\sqrt{2}}{2}\)C.\(\frac{1}{2}\)D.\(\sqrt{2}\)10.以下哪個表達式等于\(\sqrt{4}\)（）A.\(2\)B.\(-2\)C.\(\pm2\)D.\(\pm\sqrt{2}\)二、填空題（每題4分，共20分）11.計算\(\sqrt{75}\)的結果為\(\_\_\_\_\_\)。12.計算\(\sqrt{32}\)的結果為\(\_\_\_\_\_\)。13.若\(\sqrt{a}=5\)，則\(a\)的值是\(\_\_\_\_\_\)。14.計算\(\sqrt{72}\)的結果為\(\_\_\_\_\_\)。15.計算\(\sqrt{3}\times\sqrt{12}\)的結果為\(\_\_\_\_\_\)。三、解答題（每題10分，共50分）16.計算\(\sqrt{20}\div\sqrt{5}\)的結果。17.計算\(\sqrt{45}\times\sqrt{2}\)的結果。18.已知\(\sqrt{a}+\sqrt{b}=7\)，\(\sqrt{a}-\sqrt{b}=1\)，求\(a\)和\(b\)的值。19.計算\(\sqrt{24}\div\sqrt{6}\)的結果。20.計算\(\sqrt{36}+\sqrt{25}-\sqrt{49}\)的結果。答案一、選擇題1.C2.B3.A4.C5.A6.A7.B8.A9.B10.A二、填空題11.\(5\sqrt{3}\)12.\(4\sqrt{2}\)13.\(25\)14.\(6\sqrt{2}\)15.\(6\sqrt{2}\)三、解答題16.\(\sqrt{20}\div\sqrt{5}=\sqrt{4}=2\)17.\(\sqrt{45}\times\sqrt{2}=\sqrt{90}=3\sqrt{10}\)18.由題意可得：\(\sqrt{a}+\sqrt{b}=7\)和\(\sqrt{a}-\sqrt{b}=1\)，兩式相加得：\(2\sqrt{a}=8\)，所以\(\sqrt{a}=4\)，進而\(a=16\)；兩式相減得：\(2\sqrt{b}=6\)，所以\(\sqrt{b}=3\)，進而\(