Tổng hợp đáp án Chuyên đề 1 rút gọn biểu thức chứa căn
Bài 1 thực hiện phép tính
$latex 4\sqrt{5}-3\sqrt{125}+2\sqrt{45}$$latex =4\sqrt{5}-3\sqrt{5.25}+2\sqrt{5.9}$$latex =4\sqrt{5}-3.5\sqrt{5}+2.3\sqrt{5}$$latex =4\sqrt{5}-15\sqrt{5}+6\sqrt{5}$$latex =-5\sqrt{5}$
$latex 4\sqrt{5}+3\sqrt{125}-2\sqrt{45}$$latex =4\sqrt{5}+3\sqrt{5.25}-2\sqrt{5.9}$$latex =4\sqrt{5}+3.5\sqrt{5}-2.3\sqrt{5}$$latex =4\sqrt{5}+15\sqrt{5}-6\sqrt{5}$$latex =13\sqrt{5}$
| $latex 4\sqrt{5}+\sqrt{125}-2\sqrt{45}$ | $latex 4\sqrt{5}+\sqrt{125}-2\sqrt{45}$$latex =4\sqrt{5}+\sqrt{5.25}-2\sqrt{5.9}$$latex =4\sqrt{5}+.5\sqrt{5}-2.3\sqrt{5}$$latex =4\sqrt{5}+5\sqrt{5}-6\sqrt{5}$$latex =3\sqrt{5}$ |
| $latex 2\sqrt{5}+2\sqrt{125}-2\sqrt{45}$ | $latex 2\sqrt{5}+2\sqrt{125}-2\sqrt{45}$$latex =2\sqrt{5}+2\sqrt{5.25}-2\sqrt{5.9}$$latex =2\sqrt{5}+2.5\sqrt{5}-2.3\sqrt{5}$$latex =2\sqrt{5}+10\sqrt{5}-6\sqrt{5}$$latex =6\sqrt{5}$ |
| $latex 4\sqrt{3}+2\sqrt{75}-3\sqrt{27}$ | $latex 4\sqrt{3}+2\sqrt{75}-3\sqrt{27}$$latex =4\sqrt{3}+2\sqrt{3.25}-3\sqrt{3.9}$$latex =4\sqrt{3}+2.5\sqrt{3}-3.3\sqrt{3}$$latex =4\sqrt{3}+10\sqrt{3}-9\sqrt{3}$$latex =5\sqrt{3}$ |
| $latex 2\sqrt{6}+5\sqrt{384}-2\sqrt{54}$ | $latex 2\sqrt{6}+5\sqrt{384}-2\sqrt{54}$$latex =2\sqrt{6}+5\sqrt{6.64}-2\sqrt{6.9}$$latex =2\sqrt{6}+5.8\sqrt{6}-2.3\sqrt{6}$$latex =2\sqrt{6}+40\sqrt{6}-6\sqrt{6}$$latex =36\sqrt{6}$ |
| $latex 4\sqrt{5}+2\sqrt{125}-8\sqrt{125}$ | $latex 4\sqrt{5}+2\sqrt{125}-8\sqrt{125}$$latex =4\sqrt{5}+2\sqrt{5.25}-8\sqrt{5.25}$$latex =4\sqrt{5}+2.5\sqrt{5}-8.5\sqrt{5}$$latex =4\sqrt{5}+10\sqrt{5}-40\sqrt{5}$$latex =-26\sqrt{5}$ |
| $latex 2\sqrt{7}+5\sqrt{175}-8\sqrt{63}$ | $latex 2\sqrt{7}+5\sqrt{175}-8\sqrt{63}$$latex =2\sqrt{7}+5\sqrt{7.25}-8\sqrt{7.9}$$latex =2\sqrt{7}+5.5\sqrt{7}-8.3\sqrt{7}$$latex =2\sqrt{7}+25\sqrt{7}-24\sqrt{7}$$latex =3\sqrt{7}$ |
| $latex 4\sqrt{2}+4\sqrt{50}-5\sqrt{98}$ | $latex 4\sqrt{2}+4\sqrt{50}-5\sqrt{98}$$latex =4\sqrt{2}+4\sqrt{2.25}-5\sqrt{2.49}$$latex =4\sqrt{2}+4.5\sqrt{2}-5.7\sqrt{2}$$latex =4\sqrt{2}+20\sqrt{2}-35\sqrt{2}$$latex =-11\sqrt{2}$ |
| $latex 7\sqrt{1}+2\sqrt{64}-5\sqrt{9}$ | $latex 7\sqrt{1}+2\sqrt{64}-5\sqrt{9}$$latex =7\sqrt{1}+2\sqrt{1.64}-5\sqrt{1.9}$$latex =7\sqrt{1}+2.8\sqrt{1}-5.3\sqrt{1}$$latex =7\sqrt{1}+16\sqrt{1}-15\sqrt{1}$$latex =8\sqrt{1}$ |
| $latex 8\sqrt{5}+4\sqrt{320}-5\sqrt{320}$ | $latex 8\sqrt{5}+4\sqrt{320}-5\sqrt{320}$$latex =8\sqrt{5}+4\sqrt{5.64}-5\sqrt{5.64}$$latex =8\sqrt{5}+4.8\sqrt{5}-5.8\sqrt{5}$$latex =8\sqrt{5}+32\sqrt{5}-40\sqrt{5}$$latex =0\sqrt{5}$ |
| $latex 2\sqrt{325}+2\sqrt{468}-2\sqrt{117}$ | $latex 2\sqrt{325}+2\sqrt{468}-2\sqrt{117}$$latex =2\sqrt{13.25}+2\sqrt{13.36}-2\sqrt{13.9}$$latex =2.5\sqrt{13}+2.6\sqrt{13}-2.3\sqrt{13}$$latex =10\sqrt{13}+12\sqrt{13}-6\sqrt{13}$$latex =16\sqrt{13}$ |
| $latex \sqrt{5}+3\sqrt{125}-\sqrt{125}$ | $latex \sqrt{5}+3\sqrt{125}-\sqrt{125}$$latex =\sqrt{5}+3\sqrt{5.25}-\sqrt{5.25}$$latex =\sqrt{5}+3.5\sqrt{5}-.5\sqrt{5}$$latex =1\sqrt{5}+15\sqrt{5}-5\sqrt{5}$$latex =11\sqrt{5}$ |
| $latex 2\sqrt{448}+\sqrt{63}-2\sqrt{252}$ | $latex 2\sqrt{448}+\sqrt{63}-2\sqrt{252}$$latex =2\sqrt{7.64}+\sqrt{7.9}-2\sqrt{7.36}$$latex =2.8\sqrt{7}+.3\sqrt{7}-2.6\sqrt{7}$$latex =16\sqrt{7}+3\sqrt{7}-12\sqrt{7}$$latex =7\sqrt{7}$ |
| $latex 9\sqrt{125}+2\sqrt{125}-6\sqrt{45}$ | $latex 9\sqrt{125}+2\sqrt{125}-6\sqrt{45}$$latex =9\sqrt{5.25}+2\sqrt{5.25}-6\sqrt{5.9}$$latex =9.5\sqrt{5}+2.5\sqrt{5}-6.3\sqrt{5}$$latex =45\sqrt{5}+10\sqrt{5}-18\sqrt{5}$$latex =37\sqrt{5}$ |
| $latex 2\sqrt{5}+3\sqrt{125}-2\sqrt{45}$ | $latex 2\sqrt{5}+3\sqrt{125}-2\sqrt{45}$$latex =2\sqrt{5}+3\sqrt{5.25}-2\sqrt{5.9}$$latex =2\sqrt{5}+3.5\sqrt{5}-2.3\sqrt{5}$$latex =2\sqrt{5}+15\sqrt{5}-6\sqrt{5}$$latex =11\sqrt{5}$ |
| $latex 6\sqrt{5}+3\sqrt{125}-6\sqrt{180}$ | $latex 6\sqrt{5}+3\sqrt{125}-6\sqrt{180}$$latex =6\sqrt{5}+3\sqrt{5.25}-6\sqrt{5.36}$$latex =6\sqrt{5}+3.5\sqrt{5}-6.6\sqrt{5}$$latex =6\sqrt{5}+15\sqrt{5}-36\sqrt{5}$$latex =-15\sqrt{5}$ |
| $latex 2\sqrt{5}+6\sqrt{125}-2\sqrt{45}$ | $latex 2\sqrt{5}+6\sqrt{125}-2\sqrt{45}$$latex =2\sqrt{5}+6\sqrt{5.25}-2\sqrt{5.9}$$latex =2\sqrt{5}+6.5\sqrt{5}-2.3\sqrt{5}$$latex =2\sqrt{5}+30\sqrt{5}-6\sqrt{5}$$latex =26\sqrt{5}$ |
Bài 2. Rút gọn các biểu thức sau:
| $latex \sqrt { 8 – 2\sqrt 15 } + \sqrt {5 + 2\sqrt 6 } $ | $latex \sqrt { 8 – 2\sqrt 15 } + \sqrt {5 + 2\sqrt 6 } $ $latex =\sqrt {3 + 5 – 2\sqrt 3 \sqrt 5} + \sqrt {3 + 2 – 2\sqrt 3 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 3 – \sqrt 5 } \right)}^2}} + \sqrt {{{\left( {\sqrt 3 + \sqrt 2 } \right)}^2}} $ $latex =\left( {-\sqrt 3 + \sqrt 5 } \right)$+ $latex \left( {\sqrt 3 + \sqrt 2 } \right)$ $latex =\sqrt 5 – \sqrt 2 $ |
| $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {7 + 2\sqrt 10 } $ | $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {7 + 2\sqrt 10 } $ $latex =\sqrt {5 + 2 – 2\sqrt 5 \sqrt 2} + \sqrt {5 + 2 – 2\sqrt 5 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 5 – \sqrt 2 } \right)}^2}} + \sqrt {{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}} $ $latex =\left( {\sqrt 5 – \sqrt 2 } \right)$+ $latex \left( {\sqrt 5 + \sqrt 2 } \right)$ $latex =2\sqrt 5 – \sqrt 2 + \sqrt 2 $ |
| $latex \sqrt { 9 – 2\sqrt 14 } + \sqrt {5 + 2\sqrt 6 } $ | $latex \sqrt { 9 – 2\sqrt 14 } + \sqrt {5 + 2\sqrt 6 } $ $latex =\sqrt {2 + 7 – 2\sqrt 2 \sqrt 7} + \sqrt {2 + 3 – 2\sqrt 2 \sqrt 3} $ $latex =\sqrt {{{\left( {\sqrt 2 – \sqrt 7 } \right)}^2}} + \sqrt {{{\left( {\sqrt 2 + \sqrt 3 } \right)}^2}} $ $latex =\left( {-\sqrt 2 + \sqrt 7 } \right)$+ $latex \left( {\sqrt 2 + \sqrt 3 } \right)$ $latex =\sqrt 7 – \sqrt 3 $ |
| $latex \sqrt { 8 – 2\sqrt 15 } + \sqrt {10 + 2\sqrt 21 } $ | $latex \sqrt { 8 – 2\sqrt 15 } + \sqrt {10 + 2\sqrt 21 } $ $latex =\sqrt {3 + 5 – 2\sqrt 3 \sqrt 5} + \sqrt {3 + 7 – 2\sqrt 3 \sqrt 7} $ $latex =\sqrt {{{\left( {\sqrt 3 – \sqrt 5 } \right)}^2}} + \sqrt {{{\left( {\sqrt 3 + \sqrt 7 } \right)}^2}} $ $latex =\left( {-\sqrt 3 + \sqrt 5 } \right)$+ $latex \left( {\sqrt 3 + \sqrt 7 } \right)$ $latex =\sqrt 5 – \sqrt 7 $ |
| $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {9 + 2\sqrt 14 } $ | $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {9 + 2\sqrt 14 } $ $latex =\sqrt {2 + 5 – 2\sqrt 2 \sqrt 5} + \sqrt {2 + 7 – 2\sqrt 2 \sqrt 7} $ $latex =\sqrt {{{\left( {\sqrt 2 – \sqrt 5 } \right)}^2}} + \sqrt {{{\left( {\sqrt 2 + \sqrt 7 } \right)}^2}} $ $latex =\left( {-\sqrt 2 + \sqrt 5 } \right)$+ $latex \left( {\sqrt 2 + \sqrt 7 } \right)$ $latex =\sqrt 5 – \sqrt 7 $ |
| $latex \sqrt { 12 – 2\sqrt 35 } + \sqrt {9 + 2\sqrt 14 } $ | $latex \sqrt { 12 – 2\sqrt 35 } + \sqrt {9 + 2\sqrt 14 } $ $latex =\sqrt {7 + 5 – 2\sqrt 7 \sqrt 5} + \sqrt {7 + 2 – 2\sqrt 7 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 7 – \sqrt 5 } \right)}^2}} + \sqrt {{{\left( {\sqrt 7 + \sqrt 2 } \right)}^2}} $ $latex =\left( {\sqrt 7 – \sqrt 5 } \right)$+ $latex \left( {\sqrt 7 + \sqrt 2 } \right)$ $latex =2\sqrt 7 – \sqrt 5 + \sqrt 2 $ |
| $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {5 + 2\sqrt 6 } $ | $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {5 + 2\sqrt 6 } $ $latex =\sqrt {3 + 2 – 2\sqrt 3 \sqrt 2} + \sqrt {3 + 2 – 2\sqrt 3 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 3 – \sqrt 2 } \right)}^2}} + \sqrt {{{\left( {\sqrt 3 + \sqrt 2 } \right)}^2}} $ $latex =\left( {\sqrt 3 – \sqrt 2 } \right)$+ $latex \left( {\sqrt 3 + \sqrt 2 } \right)$ $latex =2\sqrt 3 – \sqrt 2 + \sqrt 2 $ |
| $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {7 + 2\sqrt 10 } $ | $latex \sqrt { 7 – 2\sqrt 10 } + \sqrt {7 + 2\sqrt 10 } $ $latex =\sqrt {5 + 2 – 2\sqrt 5 \sqrt 2} + \sqrt {5 + 2 – 2\sqrt 5 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 5 – \sqrt 2 } \right)}^2}} + \sqrt {{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}} $ $latex =\left( {\sqrt 5 – \sqrt 2 } \right)$+ $latex \left( {\sqrt 5 + \sqrt 2 } \right)$ $latex =2\sqrt 5 – \sqrt 2 + \sqrt 2 $ |
| $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {4 + 2\sqrt 4 } $ | $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {4 + 2\sqrt 4 } $ $latex =\sqrt {2 + 3 – 2\sqrt 2 \sqrt 3} + \sqrt {2 + 2 – 2\sqrt 2 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 2 – \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {\sqrt 2 + \sqrt 2 } \right)}^2}} $ $latex =\left( {-\sqrt 2 + \sqrt 3 } \right)$+ $latex \left( {\sqrt 2 + \sqrt 2 } \right)$ $latex =\sqrt 3 – \sqrt 2 $ |
| $latex \sqrt { 10 – 2\sqrt 21 } + \sqrt {5 + 2\sqrt 6 } $ | $latex \sqrt { 10 – 2\sqrt 21 } + \sqrt {5 + 2\sqrt 6 } $ $latex =\sqrt {3 + 7 – 2\sqrt 3 \sqrt 7} + \sqrt {3 + 2 – 2\sqrt 3 \sqrt 2} $ $latex =\sqrt {{{\left( {\sqrt 3 – \sqrt 7 } \right)}^2}} + \sqrt {{{\left( {\sqrt 3 + \sqrt 2 } \right)}^2}} $ $latex =\left( {-\sqrt 3 + \sqrt 7 } \right)$+ $latex \left( {\sqrt 3 + \sqrt 2 } \right)$ $latex =\sqrt 7 – \sqrt 2 $ |
| $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {9 + 2\sqrt 14 } $ | $latex \sqrt { 5 – 2\sqrt 6 } + \sqrt {9 + 2\sqrt 14 } $ $latex =\sqrt {2 + 3 – 2\sqrt 2 \sqrt 3} + \sqrt {2 + 7 – 2\sqrt 2 \sqrt 7} $ $latex =\sqrt {{{\left( {\sqrt 2 – \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {\sqrt 2 + \sqrt 7 } \right)}^2}} $ $latex =\left( {-\sqrt 2 + \sqrt 3 } \right)$+ $latex \left( {\sqrt 2 + \sqrt 7 } \right)$ $latex =\sqrt 3 – \sqrt 7 $ |
| $latex \sqrt { 9 – 2\sqrt 14 } + \sqrt {10 + 2\sqrt 21 } $ | $latex \sqrt { 9 – 2\sqrt 14 } + \sqrt {10 + 2\sqrt 21 } $ $latex =\sqrt {7 + 2 – 2\sqrt 7 \sqrt 2} + \sqrt {7 + 3 – 2\sqrt 7 \sqrt 3} $ $latex =\sqrt {{{\left( {\sqrt 7 – \sqrt 2 } \right)}^2}} + \sqrt {{{\left( {\sqrt 7 + \sqrt 3 } \right)}^2}} $ $latex =\left( {\sqrt 7 – \sqrt 2 } \right)$+ $latex \left( {\sqrt 7 + \sqrt 3 } \right)$ $latex =2\sqrt 7 – \sqrt 2 + \sqrt 3 $ |
