Thực hiện phép tính: \(\sqrt[3]{2\sqrt{14}-8}.\sqrt[3]{2\sqrt{14}+8}\)
Những câu hỏi liên quan
thực hiện phép tính \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
Bài làm:
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
\(=\sqrt{8-8\sqrt{3}+6}-\sqrt{18-12\sqrt{3}+6}\)
\(=\sqrt{\left(2\sqrt{2}-\sqrt{6}\right)^2}-\sqrt{\left(3\sqrt{2}-\sqrt{6}\right)^2}\)
\(=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}\)
\(=-\sqrt{2}\)
Học tốt
\(\sqrt{3.2-8\sqrt{3}+4.2}=\sqrt{\left(\sqrt{3}.\sqrt{2}\right)^2-2.2.\sqrt{2}.\sqrt{2}.\sqrt{3}+\left(2\sqrt{2}\right)^2}\)
\(=\sqrt{\left(2\sqrt{2}-\sqrt{6}\right)^2}-\sqrt{3^2.2-12\sqrt{3}+3.2}=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}=-\sqrt{2}\)
thực hiện phép tính:
\(\left(\sqrt{3}-2\right)\times\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
\(\sqrt{\frac{\sqrt{5}}{8\sqrt{5}+3\sqrt{35}}}\times\left(3\sqrt{2}+\sqrt{14}\right)\)
B1: thực hiện phép tínha )dfrac{sqrt{6}-sqrt{15}}{sqrt{35}-sqrt{14}}b ) dfrac{10+2sqrt{10}}{sqrt{5}+sqrt{2}}+dfrac{8}{1-sqrt{5}}c )dfrac{sqrt{3-sqrt{5}.}left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}}d ) dfrac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+dfrac{1}{sqrt{2}-sqrt{2+sqrt{3}}}B2:chúng minh vế phải bằng vế trái a) dfrac{21+8sqrt{5}}{4+sqrt{5}}.sqrt{9-4sqrt{5}}sqrt{5}-2 b) sqrt{8-2sqrt{15}}-sqrt{8+2sqrt{15}}-2sqrt{3}
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B1: thực hiện phép tính
a )\(\dfrac{\sqrt{6}-\sqrt{15}}{\sqrt{35}-\sqrt{14}}\)
b ) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
c )\(\dfrac{\sqrt{3-\sqrt{5}.}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
d ) \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2+\sqrt{3}}}\)
B2:chúng minh vế phải bằng vế trái
a) \(\dfrac{21+8\sqrt{5}}{4+\sqrt{5}}.\sqrt{9-4\sqrt{5}}=\sqrt{5}-2\)
b) \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=-2\sqrt{3}\)
Thực hiện phép tính:a)left(frac{2sqrt{3}-sqrt{6}}{sqrt{8}-2}-frac{sqrt{216}}{3}right).frac{1}{sqrt{6}}b) left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}c) frac{sqrt{5-2sqrt{6}}+sqrt{8-2sqrt{15}}}{sqrt{7+2sqrt{10}}}d) left(sqrt{28}-2sqrt{14}+sqrt{7}right).sqrt{7}+7sqrt{8}
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Thực hiện phép tính:
a)\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c) \(\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
d) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
Thêm câu này hộ tớ nx nhé !
e) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right).\left(\sqrt{2}-3\sqrt{0.4}\right)\)
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\(a,\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{12}-\sqrt{6}}{2\left(\sqrt{2}-1\right)}-\frac{6\sqrt{6}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-2\sqrt{6}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}}{2}-\frac{4\sqrt{6}}{2}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{\sqrt{6}-4\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{-3\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=-\frac{3}{2}\)
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\(b,\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
\(=\left(\frac{\sqrt{7}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}+\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\right).\left(\sqrt{7}-\sqrt{5}\right)\)
\(=\left(\frac{-\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\right).\left(\sqrt{7}-\sqrt{5}\right)\)
\(=\left(-\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(7-5\right)\)
\(=-2\)
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thực hiện phép tính:
a)\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
b)\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c)\(\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
a) Kết quả rút gọn xấu (+dài) nữa. (có thể đề sai)
b)
\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
\(=\left[\frac{-\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\frac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right].\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)=-\left(7-5\right)=-2\)
c) \(\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}=\frac{\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}}\)
\(=\frac{\sqrt{3}-\sqrt{2}+\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}=\frac{\left(\sqrt{5}-\sqrt{2}\right)^2}{3}\)
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a) \(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}=\left[\frac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-2\sqrt{6}\right].\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}}{2}-2\sqrt{6}\right).\frac{1}{\sqrt{6}}=\frac{1}{2}-2=-\frac{3}{2}\)
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1) thực hiện phép tính
a) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
b) \(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
c) \(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}\)
giúp mk vs ạ mk đang cần gấp
a)\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
\(=2.\sqrt{\dfrac{4^2}{3}}-3.\sqrt{\dfrac{1}{3.3^2}}-6\sqrt{\dfrac{2^2}{3.5^2}}\)
\(=2.\dfrac{4}{\sqrt{3}}-3.\dfrac{1}{3\sqrt{3}}-6.\dfrac{2}{5\sqrt{3}}=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}\)\(=\dfrac{23}{5\sqrt{3}}=\dfrac{23\sqrt{3}}{15}\)
b)\(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{8}{9}.\dfrac{1}{2}}-5\sqrt{\dfrac{32}{25}.\dfrac{1}{2}}+14\sqrt{\dfrac{18}{49}.\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{4}{9}}-5\sqrt{\dfrac{16}{25}}+14\sqrt{\dfrac{9}{49}}\)\(=6.\dfrac{2}{3}-5.\dfrac{4}{5}+14.\dfrac{3}{7}=6\)
c)\(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}=\left|\sqrt{2}-2\right|-\sqrt{4+2.2\sqrt{2}+2}=2-\sqrt{2}-\sqrt{\left(2+\sqrt{2}\right)^2}\)
\(=2-\sqrt{2}-\left(2+\sqrt{2}\right)=-2\sqrt{2}\)
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thực hiện phép tính
a)\(3\sqrt{9-\sqrt{25}+2\sqrt{49}}\)
b)\(7\sqrt[3]{27}-\sqrt[3]{64}+2\sqrt[3]{8}\)
c)\(\left(\sqrt{28}+2\sqrt{14}+3\sqrt{7}\right)\left(\sqrt{7}-7\sqrt{8}\right)\)
d)\(\frac{6\sqrt{7}+\sqrt{12}}{2}+\sqrt{7}+\sqrt{67-12\sqrt{7}}\)
Thực hiện phép tính:a,left(sqrt{28}-2sqrt{14}+sqrt{7}right)cdotsqrt{7}+7sqrt{8}b,left(sqrt{8}-3sqrt{2}+sqrt{10}right)cdotleft(sqrt{2}-3sqrt{0.4}right)c,left(15sqrt{50}+5sqrt{200}-3sqrt{450}right):sqrt{10}d,sqrt{6+2sqrt{5}}+sqrt{6-2sqrt{5}}e,sqrt{11+6sqrt{2}}-sqrt{11-6sqrt{2}}f,sqrt[3]{5sqrt{2}+7}-sqrt[3]{5sqrt{2}-7}g,sqrt[3]{20+14sqrt{2}}+sqrt[3]{20-14sqrt{2}}h,sqrt[3]{26+15sqrt{3}}-sqrt[3]{26-15sqrt{3}}
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Thực hiện phép tính:
\(a,\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(b,\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\cdot\left(\sqrt{2}-3\sqrt{0.4}\right)\)
\(c,\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)
\(d,\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
\(e,\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(f,\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
\(g,\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
\(h,\sqrt[3]{26+15\sqrt{3}}-\sqrt[3]{26-15\sqrt{3}}\)
g, h. Câu hỏi của Nữ hoàng sến súa là ta - Toán lớp 9 - Học toán với OnlineMath
thực hiện phép tính :
(2\(\sqrt{6}\) - 4\(\sqrt{3}\) + 5\(\sqrt{2}\) - \(\dfrac{1}{4}\)\(\sqrt{8}\)) . 3\(\sqrt{6}\)
\(=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{\sqrt{2}}{2}\right)\cdot3\sqrt{6}\\ =36-36\sqrt{2}+30\sqrt{3}-3\sqrt{3}\\ =36-36\sqrt{2}+27\sqrt{3}\)
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