【中学3年数学】2-2 平方根の計算｜問題集
1.次の数を簡略化しなさい。
(1)\(\sqrt{20}\)
(2)\(\sqrt{44}\)
(3)\(\sqrt{75}\)
(4)\(\sqrt{48}\)
(5)\(\sqrt{72}\)
(6)\(\displaystyle \sqrt{\frac{7}{100}}\)
(7)\(\sqrt{45}\)
(8)\(\sqrt{54}\)
(9)\(\sqrt{128}\)
2.次の数の分母を有理化しなさい。
(1)\(\displaystyle \frac{2}{\sqrt{5}}\)
(2)\(\displaystyle \frac{\sqrt{8}}{\sqrt{7}}\)
(3)\(\displaystyle \frac{\sqrt{3}}{2\sqrt{10}}\)
(4)\(\displaystyle \frac{4}{\sqrt{3}}\)
(5)\(\displaystyle -\frac{\sqrt{7}}{\sqrt{6}}\)
(6)\(\displaystyle \frac{5\sqrt{2}}{\sqrt{10}}\)
(7)\(\displaystyle \frac{5}{\sqrt{3}}\)
(8)\(\displaystyle \frac{7}{\sqrt{7}}\)
(9)\(\displaystyle \frac{2\sqrt{3}}{\sqrt{2}}\)
3.次の計算をしなさい。
(1)\(\sqrt{5}\sqrt{6}\)
(2)\(\sqrt{3}\sqrt{7}\)
(3)\(\sqrt{2}\sqrt{13}\)
(4)\(\sqrt{11}\sqrt{5}\)
(5)\(\sqrt{2}\sqrt{5}\sqrt{7}\)
(6)\(\sqrt{6}\sqrt{11}\sqrt{7}\)
(7)\(\sqrt{10}÷\sqrt{6}\)
(8)\(\sqrt{15}÷\sqrt{35}\)
(9)\(\sqrt{42}÷\sqrt{22}\)
(10)\(\sqrt{26}÷\sqrt{20}\)
(11)\(\sqrt{14}÷\sqrt{7}\)
(12)\(\sqrt{12}÷\sqrt{3}\)
(13)\(\sqrt{8}\sqrt{75}\)
(14)\(\sqrt{45}\sqrt{18}\)
(15)\(\sqrt{108}\sqrt{28}\)
(16)\(\sqrt{75}÷\sqrt{24}\)
(17)\(\sqrt{56}÷\sqrt{40}\)
(18)\(\sqrt{32}÷\sqrt{50}\)
(19)\(\sqrt{18}÷\sqrt{21}\)
(20)\(3\sqrt{5}÷\sqrt{3}\)
(21)\(2\sqrt{7}÷\sqrt{6}\)
(22)\(\sqrt{24}\sqrt{27}\)
(23)\(\sqrt{12}\sqrt{20}\sqrt{8}\)
(24)\(4\sqrt{6}÷\sqrt{12}\)
(25)\(\sqrt{54}÷\sqrt{6}\)
(26)\(5\sqrt{6}+3\sqrt{6}\)
(27)\(8\sqrt{10}+2\sqrt{10}\)
(28)\(7\sqrt{3}-4\sqrt{3}\)
(29)\(2\sqrt{7}-9\sqrt{7}\)
(30)\(3\sqrt{2}+4\sqrt{2}+\sqrt{2}\)
(31)\(6\sqrt{5}-\sqrt{5}-2\sqrt{5}\)
(32)\(\sqrt{48}+\sqrt{75}\)
(33)\(\sqrt{45}-\sqrt{20}\)
(34)\(\sqrt{28}+\sqrt{63}-\sqrt{7}\)
(35)\(\sqrt{24}+\sqrt{6}-\sqrt{96}\)
(36)\(\sqrt{27}+\sqrt{7}+\sqrt{3}-\sqrt{28}\)
(37)\(\sqrt{32}-3\sqrt{6}-\sqrt{18}+4\sqrt{6}\)
(38)\(\sqrt{45}-\sqrt{8}+\sqrt{20}-\sqrt{50}\)
(39)\(\sqrt{75}-\sqrt{54}+\sqrt{96}-\sqrt{108}\)
(40)\(\displaystyle \sqrt{8}-\frac{2}{\sqrt{2}}\)
(41)\(\displaystyle \sqrt{24}+\frac{2\sqrt{2}}{\sqrt{3}}\)
(42)\(\displaystyle \frac{\sqrt{5}}{\sqrt{2}}-\frac{\sqrt{2}}{\sqrt{5}}+\sqrt{10}\)
(43)\(\sqrt{7}\sqrt{35}\)
(44)\(\sqrt{24}\sqrt{80}\)
(45)\(\sqrt{8}\sqrt{50}\sqrt{27}\)
(46)\(\sqrt{30}÷\sqrt{12}\)
(47)\(\sqrt{48}÷\sqrt{18}\)
(48)\(\sqrt{6}\sqrt{20}÷\sqrt{15}\)
(49)\(5\sqrt{5}-7\sqrt{5}\)
(50)\(\sqrt{3}-\sqrt{12}+\sqrt{27}\)
(51)\(2\sqrt{3}-\sqrt{45}+\sqrt{27}-\sqrt{80}\)
(52)\(\displaystyle \frac{1}{\sqrt{5}}+\frac{1}{3\sqrt{3}}+\sqrt{3}\)
(53)\(\sqrt{7}(\sqrt{2}+\sqrt{5})\)
(54)\(\sqrt{2}(\sqrt{3}-2\sqrt{6})\)
(55)\(\sqrt{8}(\sqrt{12}+\sqrt{6})\)
(56)\(3\sqrt{3}(\sqrt{50}+\sqrt{75})\)
(57)\((\sqrt{7}+3)(\sqrt{7}+2)\)
(58)\((\sqrt{2}-1)^2\)
(59)\((2\sqrt{5}-3)(2\sqrt{5}+3)\)
(60)\((\sqrt{3}+1)^2-2(\sqrt{3}+1)\)
(61)\(\sqrt{3}(\sqrt{6}-\sqrt{12})\)
(62)\((\sqrt{48}+\sqrt{27})÷2\sqrt{3}\)
(63)\((2+\sqrt{7})(2-\sqrt{7})\)
(64)\((2\sqrt{5}+1)^2\)
(65)\((\sqrt{3}-1)(\sqrt{3}+8)\)
(66)\((2+\sqrt{6})(-3+\sqrt{6})\)
(67)\((\sqrt{3}+\sqrt{5})^2\)
(68)\((\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2})\)
(69)\((3-\sqrt{2}+\sqrt{5})^2\)
(70)\((2-\sqrt{6})^2-4(2-\sqrt{6})+4\)
4.\(\sqrt{3}=1.732,\sqrt{30}=5.477\)とするとき、次の値を求めなさい。
(1)\(\sqrt{3000}\)
(2)\(\sqrt{30000}\)
(3)\(\sqrt{0.3}\)
5.\(\sqrt{5.2}=2.280,\sqrt{52}=7.211\)とするとき、次の値を求めなさい。
(1)\(\sqrt{520}\)
(2)\(\sqrt{520000}\)
(3)\(\sqrt{0.0052}\)
6.\(x=\sqrt{3}+1,y=\sqrt{3}-1\)とするとき、次の値を求めなさい。
(1)\(x^2+2xy+y^2\)
(2)\(x^2-y^2\)
7.\(x=\sqrt{3}+\sqrt{2},y=\sqrt{3}-\sqrt{2}\)とするとき、次の値を求めなさい。
(1)\(3x^2-3y^2\)
(2)\(2x^2-4xy+2y^2\)
次の学習に進もう！