tính
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
Những câu hỏi liên quan
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
Thực hiện phép tính
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}=0\)
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\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
Thực hiện phép tính:
\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)\)
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(=\sqrt{\frac{6-2\sqrt{5}}{2}}+\sqrt{\frac{6+2\sqrt{5}}{2}}\)
\(=\sqrt{\frac{5-2\sqrt{5}+1}{2}}+\sqrt{\frac{5+2\sqrt{5}+1}{2}}\)
\(=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)
\(=\frac{\sqrt{5}-1}{\sqrt{2}}+\frac{\sqrt{5}+1}{\sqrt{2}}\)
\(=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{2}.\sqrt{2}.\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)
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a. \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
b. \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)
chúc bạn học tốt:)
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Ai giải cho mình phép này với, mình không biết bắt đầu từ đâu:
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
\(\sqrt{2}\sqrt{4}\sqrt{3}+2.5\sqrt{4}\sqrt{3}-4\sqrt{16}\sqrt{4}\sqrt{3}=2\sqrt{6}+10\sqrt{12}-16\sqrt{12}=2\sqrt{6}-6\sqrt{12}=2\sqrt{6}-12\sqrt{3}\)
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thực hiện phép tínha, dfrac{sqrt{3-sqrt{5}}.left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}}b, sqrt{8sqrt{3}}-2sqrt{25sqrt{12}}+4sqrt{sqrt{192}}c, sqrt{2-sqrt{3}}.left(sqrt{5}+sqrt{2}right)d, sqrt{3-sqrt{5}}+sqrt{3+sqrt{5}}e, sqrt{4+sqrt{10+2sqrt{5}}}+sqrt{4-sqrt{10+2sqrt{5}}}f, left(5+2sqrt{6}right)left(49-20sqrt{6}right)sqrt{5-2sqrt{6}}g, dfrac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+dfrac{1}{sqrt{2}-sqrt{2-sqrt{3}}}h, dfrac{6+4sqrt{2}}{sqrt{2}+sqrt{6+4sqrt{2}}}+dfrac{6-4sqrt{2}}{sqrt{2}+sqrt{6+4sqrt{2}}}i, dfrac{...
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thực hiện phép tính
a, \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b, \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
c, \(\sqrt{2-\sqrt{3}}.\left(\sqrt{5}+\sqrt{2}\right)\)
d, \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
e, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
f, \(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
g, \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
h, \(\dfrac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}\)
i, \(\dfrac{\left(\sqrt{5+2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
k, \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
l, \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}\)
m, \(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
n, \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3+1}}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3+1}}}\)
h. \(\sqrt{5}+\sqrt{9-4\sqrt{5}}\)
i. \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
h)\(\sqrt{5}+\sqrt{9-4\sqrt{5}}=\sqrt{5}+\sqrt{\left(\sqrt{5}\right)^2-2.2.\sqrt{5}+2^2}\)
\(=\sqrt{5}+\sqrt{\left(\sqrt{5-2}\right)^2}\)
\(=\sqrt{5}+\left|\sqrt{5}-2\right|\)
\(=\sqrt{5}+\sqrt{5}-2\)
\(=2\sqrt{5}-2\)
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i. \(2\sqrt{2\sqrt{3}}-10\sqrt{2\sqrt{3}}+8\sqrt{2\sqrt{3}}=\sqrt{2\sqrt{3}}\left(2-10+8\right)\)
\(=\sqrt{2\sqrt{3}}.0=0\)
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Thực hiện phép tính:
a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
b) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
c) \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
a)\(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
= \(2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}\)
= \(4\sqrt{5}\)
b) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
= \(\sqrt{3\left(5-2\sqrt{6}\right)}-\sqrt{33-12\sqrt{6}}\)
= \(\sqrt{3\left(5-2\sqrt{6}\right)}-\sqrt{3\left(11-4\sqrt{6}\right)}\)
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\(a,2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
\(=2\sqrt{5}-\sqrt{5^2.5}-\sqrt{4^2.5}+\sqrt{11^2.5}\)
\(=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}\)
\(=4\sqrt{5}\)
\(b,\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
\(=\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3-2\sqrt{6}\right)^2}\)
\(=|3-\sqrt{6}|+|3-2\sqrt{6}|\)
\(=3-\sqrt{6}+2\sqrt{6}-3\)
\(=\sqrt{6}\)
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