二次根式檢測題pdf試卷及答案一、選擇題（每題3分，共30分）1.計算下列二次根式：A.\(\sqrt{4}=2\)B.\(\sqrt{9}=3\)C.\(\sqrt{16}=4\)D.\(\sqrt{25}=5\)答案：B2.以下哪個選項是正確的二次根式化簡？A.\(\sqrt{8}=2\sqrt{2}\)B.\(\sqrt{12}=3\sqrt{2}\)C.\(\sqrt{18}=3\sqrt{3}\)D.\(\sqrt{24}=2\sqrt{6}\)答案：A3.計算下列二次根式的乘積：A.\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\)B.\(\sqrt{3}\times\sqrt{4}=2\sqrt{3}\)C.\(\sqrt{5}\times\sqrt{5}=5\)D.\(\sqrt{7}\times\sqrt{7}=7\)答案：A4.以下哪個選項是正確的二次根式除法？A.\(\frac{\sqrt{15}}{\sqrt{3}}=\sqrt{5}\)B.\(\frac{\sqrt{20}}{\sqrt{4}}=\sqrt{5}\)C.\(\frac{\sqrt{21}}{\sqrt{7}}=\sqrt{3}\)D.\(\frac{\sqrt{28}}{\sqrt{7}}=2\sqrt{2}\)答案：C5.計算下列二次根式的和：A.\(\sqrt{2}+\sqrt{3}=\sqrt{5}\)B.\(\sqrt{4}+\sqrt{9}=5\)C.\(\sqrt{6}+\sqrt{8}=2\sqrt{7}\)D.\(\sqrt{10}+\sqrt{15}=5\sqrt{2}\)答案：B6.以下哪個選項是正確的二次根式減法？A.\(\sqrt{10}-\sqrt{9}=\sqrt{1}\)B.\(\sqrt{12}-\sqrt{4}=2\sqrt{2}\)C.\(\sqrt{18}-\sqrt{9}=3\sqrt{2}\)D.\(\sqrt{24}-\sqrt{16}=2\sqrt{2}\)答案：C7.計算下列二次根式的平方：A.\((\sqrt{7})^2=49\)B.\((\sqrt{8})^2=64\)C.\((\sqrt{9})^2=81\)D.\((\sqrt{11})^2=121\)答案：B8.以下哪個選項是正確的二次根式混合運算？A.\(\sqrt{2}\times\sqrt{3}+\sqrt{5}=2\sqrt{3}+\sqrt{5}\)B.\(\sqrt{4}-\sqrt{9}+\sqrt{16}=0+4=4\)C.\(\sqrt{6}\div\sqrt{2}-\sqrt{3}=\sqrt{3}-\sqrt{3}=0\)D.\(\sqrt{7}\times\sqrt{7}-\sqrt{8}=7-2\sqrt{2}\)答案：D9.計算下列二次根式的立方：A.\((\sqrt{2})^3=8\)B.\((\sqrt{3})^3=27\)C.\((\sqrt{4})^3=64\)D.\((\sqrt{5})^3=125\)答案：C10.以下哪個選項是正確的二次根式方程的解？A.\(\sqrt{x}=4\)的解是\(x=16\)B.\(\sqrt{x}=9\)的解是\(x=81\)C.\(\sqrt{x}=12\)的解是\(x=144\)D.\(\sqrt{x}=15\)的解是\(x=225\)答案：A二、填空題（每題4分，共40分）11.計算\(\sqrt{34}\)的值，保留兩位小數。答案：5.8312.化簡\(\sqrt{75}\)。答案：\(5\sqrt{3}\)13.計算\(\sqrt{48}\div\sqrt{12}\)的值。答案：\(2\sqrt{3}\)14.計算\(\sqrt{27}+\sqrt{81}\)的值。答案：1515.計算\((\sqrt{2}-\sqrt{3})^2\)的值。答案：8-4\(\sqrt{6}\)16.計算\(\sqrt{3}\times\sqrt{12}\)的值。答案：617.計算\(\sqrt{50}-\sqrt{18}\)的值。答案：\(\sqrt{2}\)18.計算\((\sqrt{5}+2)(\sqrt{5}-2)\)的值。答案：119.計算\(\sqrt{72}\div\sqrt{8}\)的值。答案：320.計算\(\sqrt{32}\times\sqrt{2}\)的值。答案：8三、解答題（每題15分，共30分）21.解方程\(\sqrt{x}+3=7\)。解：首先將方程兩邊同時減去3，得到\(\sqrt{x}=4\)。然后兩邊平方，得到\(x=16\)。答案：\(x=16\)22.已知\(\sqrt{a}=2\)和