a: \(=\sqrt{17^2\cdot21}=17\sqrt{21}\)
b: \(=\sqrt{2.5\cdot2.5\cdot5\cdot20}=2.5\cdot10=25\)
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Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Rút gọn căn cho một số bằng phép khai phương
1) \(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
Bài 5: Rút gọn căn cho một số bằng phép khai phương
9 sqrt{12} + sqrt{75} - sqrt{27}
10 sqrt{27} - sqrt{12} + sqrt{75} + sqrt{147}
11 2sqrt{3} + sqrt{48} - sqrt{75} - sqrt{243}
12 sqrt{5+2sqrt{6}} - sqrt{5-2sqrt{6}}
13 sqrt{9-4sqrt{5}} - sqrt{9+sqrt{80}}
14 sqrt{3+2sqrt{2}} _ sqrt{6-4sqrt{2}}
15 sqrt{17-4sqrt{9+4sqrt{5}}}
16 sqrt{4+sqrt{5}sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}
17 (sqrt{28} - 2sqrt{14} + sqrt{7})sqrt{7} + 7sqrt{8}
18 sqrt{left(sqrt{14}-3sqrt{2}right)^2}+6sqrt{28}
19 df...
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Bài 5: Rút gọn căn cho một số bằng phép khai phương
9> \(\sqrt{12}\) + \(\sqrt{75}\) - \(\sqrt{27}\)
10> \(\sqrt{27}\) - \(\sqrt{12}\) + \(\sqrt{75}\) + \(\sqrt{147}\)
11> \(2\sqrt{3}\) + \(\sqrt{48}\) - \(\sqrt{75}\) - \(\sqrt{243}\)
12> \(\sqrt{5+2\sqrt{6}}\) - \(\sqrt{5-2\sqrt{6}}\)
13> \(\sqrt{9-4\sqrt{5}}\) - \(\sqrt{9+\sqrt{80}}\)
14> \(\sqrt{3+2\sqrt{2}}\) _ \(\sqrt{6-4\sqrt{2}}\)
15> \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
16> \(\sqrt{4+\sqrt{5}\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
17> (\(\sqrt{28}\) - \(2\sqrt{14}\) + \(\sqrt{7}\))\(\sqrt{7}\) + 7\(\sqrt{8}\)
18> \(\sqrt{\left(\sqrt{14}-3\sqrt{2}\right)^2}+6\sqrt{28}\)
19> \(\dfrac{1}{\sqrt{5}-2}\) + \(\dfrac{1}{\sqrt{5}+2}\)
20> \(\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5-\sqrt{3}}}\) + \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
21> \(\dfrac{1}{4-3\sqrt{2}}\) _ \(\dfrac{1}{4+3\sqrt{2}}\)
22> \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
Rút gọn:
a) sqrt{24-3sqrt{15}}-sqrt{36-9sqrt{15}}
b)sqrt{2-sqrt{3}}-sqrt{2+sqrt{3}}
c)sqrt{3-sqrt{5}}-sqrt{3+sqrt{5}}
d) sqrt{9-sqrt{17}}-sqrt{9+sqrt{17}}
e) sqrt{7+sqrt{13}}-sqrt{7-sqrt{13}}
f) sqrt{12-3sqrt{7}}-sqrt{12+3sqrt{7}}
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Rút gọn:
a) \(\sqrt{24-3\sqrt{15}}-\sqrt{36-9\sqrt{15}}\)
b)\(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
c)\(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
d) \(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}\)
e) \(\sqrt{7+\sqrt{13}}-\sqrt{7-\sqrt{13}}\)
f) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
Bài: thực hiện phép tính
a. \(\dfrac{12}{1+\sqrt[]{5}}+\dfrac{15}{\sqrt[]{5}}-\dfrac{\sqrt[]{20}-5}{2-\sqrt[]{5}}\)
b. \(\dfrac{2\sqrt[]{x}}{\sqrt[]{x}-1}-\dfrac{3x}{x-\sqrt[]{x}}+\dfrac{1}{\sqrt[]{x}}\left(x>0,x\ne1\right)\)
Áp dụng quy tắc khai phương một tích, hãy tính:
a) \sqrt{3.75}
b) \sqrt{0,4.6,4}
c) \sqrt{12,1.360}
d) \sqrt{49.1,44.25}
g) \sqrt{2,7.5.1,5}
e) \sqrt{1,3.52.10}
Giải phương trình sau:
a) \(\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)
b) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6\)
So sánh A = 2\(\sqrt{1}+2\sqrt{3}+2\sqrt{5}+2\sqrt{7}+2\sqrt{9}+2\sqrt{11}+2\sqrt{13}+2\sqrt{15}+2\sqrt{17}+2\sqrt{19}\) và B = \(2\sqrt{2}+2\sqrt{4}+2\sqrt{6}+2\sqrt{8}+2\sqrt{10}+2\sqrt{12}+2\sqrt{14}+2\sqrt{16}+2\sqrt{18}+2\sqrt{20}\)
Bài 1: Rút gọn căn cho một phép khai phương
a> \(3\sqrt{50}\) - \(2\sqrt{12}\) - \(\sqrt{18}\) + \(\sqrt{75}\) - \(\sqrt{8}\)
Tính thu gọn :
a , sqrt{17-12sqrt{2}}-sqrt{17+12sqrt{2}}
b , sqrt{27+12sqrt{5}}-sqrt{27-12sqrt{5}}
c , sqrt{15-6sqrt{6}}+sqrt{15+sqrt{6sqrt{6}}}
d , sqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}
e , sqrt{17-3sqrt{32}}+sqrt{17+3sqrt{32}}
f , sqrt{5+sqrt{3-sqrt{29-12sqrt{5}}}}
Đọc tiếp
Tính thu gọn :
a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)
c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)
d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)