Tính:
a) \(\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3}-\sqrt{2}}\)
b)\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}\)
Những câu hỏi liên quan
Tính Q=\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
Tính giá trị biểu thức
A = \(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
B = \(\frac{1}{\sqrt{2}-\sqrt{3}}\cdot\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
rút gọn A =\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
Ta có: \(A=\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(=\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)^2}{\left(\sqrt{5+3\sqrt{2}}\right)^2-\left(\sqrt{5-3\sqrt{2}}\right)^2}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)^2}{\left(\sqrt{3+\sqrt{2}}\right)^2-\left(\sqrt{3-\sqrt{2}}\right)^2}\)
\(=\frac{3\left[\left(\sqrt{5+3\sqrt{2}}\right)^2+2\cdot\sqrt{5+3\sqrt{2}}\cdot\sqrt{5-3\sqrt{2}}+\left(\sqrt{5-3\sqrt{2}}\right)^2\right]}{\left|5+3\sqrt{2}\right|-\left|5-3\sqrt{2}\right|}-\frac{\left(\sqrt{3+\sqrt{2}}\right)^2+2\cdot\sqrt{3+\sqrt{2}}\cdot\sqrt{3-\sqrt{2}}+\left(\sqrt{3-\sqrt{2}}\right)^2}{\left|3+\sqrt{2}\right|-\left|3-\sqrt{2}\right|}\)
\(=\frac{3\left(\left|5+3\sqrt{2}\right|+2\sqrt{7}+\left|5-3\sqrt{2}\right|\right)}{5+3\sqrt{2}-\left(5-3\sqrt{2}\right)}-\frac{\left|3+\sqrt{2}\right|+2\cdot\sqrt{7}+\left|3-\sqrt{2}\right|}{3+\sqrt{2}-\left(3-\sqrt{2}\right)}\)
\(=\frac{3\left(5+3\sqrt{2}+2\sqrt{7}+5-3\sqrt{2}\right)}{5+3\sqrt{2}-5+3\sqrt{2}}-\frac{3+\sqrt{2}+2\sqrt{7}+3-\sqrt{2}}{3+\sqrt{2}-3+\sqrt{2}}\)
\(=\frac{3\left(10+2\sqrt{7}\right)}{6\sqrt{2}}-\frac{6+2\sqrt{7}}{2\sqrt{2}}\)
\(=\frac{3\left(10+2\sqrt{7}\right)}{6\sqrt{2}}-\frac{3\left(6+2\sqrt{7}\right)}{6\sqrt{2}}\)
\(=\frac{30+6\sqrt{7}-18-6\sqrt{7}}{6\sqrt{2}}\)
\(=\frac{12}{6\sqrt{2}}=\sqrt{2}\)
Vậy: \(A=\sqrt{2}\)
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Tính :\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
ai làm đúng mình tick
Tính
\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(\sqrt{\sqrt{11}+1}.\sqrt{\sqrt{11}-1}+\sqrt{10}\)
\(\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(=\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)}{\left(\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}\right)\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)}{\left(\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}\right)\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)}\)
\(=\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)^2}{5+3\sqrt{2}-\left(5-3\sqrt{2}\right)}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)^2}{3+\sqrt{2}-\left(3-\sqrt{2}\right)}\)
\(=\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)^2}{6\sqrt{2}}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)^2}{2\sqrt{2}}\)
\(=\frac{\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)^2}{2\sqrt{2}}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)^2}{2\sqrt{2}}\)
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\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(=\frac{3\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(=\frac{\left(\sqrt{5+3\sqrt{2}}+\sqrt{5-3\sqrt{2}}\right)^2}{2\sqrt{2}}-\frac{\left(\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}\right)^2}{2\sqrt{2}}\)
\(=\frac{10+2\sqrt{7}-6-2\sqrt{7}}{2\sqrt{2}}=\sqrt{2}\)
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\(\sqrt{\sqrt{11}+1}.\sqrt{\sqrt{11}-1}+\sqrt{10}=\sqrt{10}+\sqrt{10}=2\sqrt{10}\)
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rút gọn các căn thức sauBfrac{sqrt{5-sqrt{3}}-sqrt{5+sqrt{3}}}{sqrt{5-sqrt{22}}}+sqrt{27+10sqrt{2}}C frac{sqrt{45+27sqrt{2}}+sqrt{45-27sqrt{2}}}{sqrt{5+3sqrt{2}}-sqrt{5-3sqrt{2}}}-frac{sqrt{3+sqrt{2}}+sqrt{3-sqrt{2}}}{sqrt{3+sqrt{2}}-sqrt{3-sqrt{2}}}Dfrac{1}{sqrt{2}-sqrt{3}}.sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}}A frac{1}{sqrt{3+2sqrt{2}}}+frac{1}{sqrt{5+2sqrt{6}}}+frac{1}{sqrt{7+2sqrt{12}}}+....+frac{1}{sqrt{199+2sqrt{9900}}}
Đọc tiếp
rút gọn các căn thức sau
B=\(\frac{\sqrt{5-\sqrt{3}}-\sqrt{5+\sqrt{3}}}{\sqrt{5-\sqrt{22}}}+\sqrt{27+10\sqrt{2}}\)C= \(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)D=\(\frac{1}{\sqrt{2}-\sqrt{3}}.\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)A= \(\frac{1}{\sqrt{3+2\sqrt{2}}}+\frac{1}{\sqrt{5+2\sqrt{6}}}+\frac{1}{\sqrt{7+2\sqrt{12}}}+....+\frac{1}{\sqrt{199+2\sqrt{9900}}}\)
Thu gọn biểu thức:
\(A=\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
\(B=\sqrt{\left(1-\sqrt{2020}\right)^2}.\sqrt{2021+2\sqrt{2020}}\)
\(C=\sqrt{\sqrt{3}-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Tính a) A ^{sqrt[3]{5sqrt{2}+7}-sqrt[3]{5sqrt{2}-7}+sqrt{10+sqrt{19}}-sqrt{10-sqrt{19}}} b) B frac{sqrt{45+27sqrt{2}}+sqrt{45-27sqrt{2}}}{sqrt{5+3sqrt{2}}-sqrt{5-3sqrt{2}}}-frac{sqrt{3+sqrt{2}}+sqrt{3-sqrt{2}}}{sqrt{3+sqrt{2}-sqrt{3-sqrt{2}}}}
Đọc tiếp
Tính
a) A = \(^{\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}+\sqrt{10+\sqrt{19}}-\sqrt{10-\sqrt{19}}}\) b) B = \(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}-\sqrt{3-\sqrt{2}}}}\)
Rút gọn biểu thức:
\(a,\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
\(b,\frac{1+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{1-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)