tính
\(\sqrt{2}\) ✖ (\(\sqrt{21}+3\)) ✖ \(\sqrt{5-\sqrt{21}}\)
\(\sqrt{2}\times\left(\sqrt{5}-1\right)\times\sqrt{3+\sqrt{5}}\)
Những câu hỏi liên quan
sqrt{46-6sqrt{5}}-sqrt{29-12sqrt{5}} sqrt{13-sqrt{160}-sqrt{53+4sqrt{90}}} left(sqrt{3+}sqrt{5}right)timessqrt{7-2sqrt{10}}...
Đọc tiếp
\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\) \(\sqrt{13-\sqrt{160}-\sqrt{53+4\sqrt{90}}}\) \(\left(\sqrt{3+}\sqrt{5}\right)\times\sqrt{7-2\sqrt{10}}\) \(\left(\sqrt{7}-\sqrt{3}\right)\times\sqrt{10+2\sqrt{21}}\)
Mình làm luôn nhé :
\(\sqrt{45-2.3\sqrt{5}+1}-\sqrt{20-2.3.2\sqrt{5}+9}\sqrt{8-2.2\sqrt{2}.\sqrt{5}+5-\sqrt{45+2.2.\sqrt{2}.3\sqrt{5}+8}}\left(\sqrt{3}+\sqrt{5}\right).\sqrt{5-2.\sqrt{5}.\sqrt{2}+2}\left(\sqrt{7}-\sqrt{3}\right).\sqrt{7+2.\sqrt{7}.\sqrt{3}+3}\) Tới đây dễ rồi , bạn tự nhóm HĐT là ra ::v
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câu a sqrt{46-6sqrt{5}}-sqrt{29-12sqrt{5}} câu b sqrt{13-sqrt{160}}-sqrt{53+4sqrt{90}} câu c left(sqrt{3}+sqrt{5}right)timessqrt{7-2sqrt{10}}...
Đọc tiếp
câu a \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\) câu b \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\) câu c \(\left(\sqrt{3}+\sqrt{5}\right)\times\sqrt{7-2\sqrt{10}}\) câu d \(\left(\sqrt{7}-\sqrt{3}\right)\times\sqrt{10+2\sqrt{21}}\)
à
Tính :
1)\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
2)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
3)\(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right).\sqrt{\sqrt{3}+2}\)
4)\(\left(5+\sqrt{21}\right).\left(\sqrt{14}-\sqrt{6}\right).\sqrt{5-\sqrt{21}}\)
a)\(\left(\sqrt{21}+7\right)\cdot\sqrt{10-2\sqrt{21}}\)
\(=\left(\sqrt{21}+7\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\sqrt{7}\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{7}\left(7-3\right)=4\sqrt{7}\)
b)\(\left(7+\sqrt{14}\right)\sqrt{9-2\sqrt{14}}\)
\(=\left(7+\sqrt{14}\right)\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)
\(=\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)\)
\(=\sqrt{7}\left(7-2\right)=5\sqrt{7}\)
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\(\left(\dfrac{\sqrt{7}-1}{\sqrt{21}-\sqrt{3}}+\dfrac{\sqrt{3}-1}{\sqrt{21}-\sqrt{7}}\right)\times\dfrac{\sqrt{21}}{\sqrt{7}+\sqrt{3}}\)
\(=\left[\dfrac{\sqrt{7}-1}{\sqrt{3}\left(\sqrt{7}-1\right)}+\dfrac{\sqrt{3}-1}{\sqrt{7}\left(\sqrt{3}-1\right)}\right]\cdot\dfrac{\sqrt{21}}{\sqrt{7}+\sqrt{3}}\\ =\left(\dfrac{1}{\sqrt{3}}+\dfrac{1}{\sqrt{7}}\right)\cdot\dfrac{\sqrt{21}}{\sqrt{7}+\sqrt{3}}\\ =\dfrac{\sqrt{3}+\sqrt{7}}{\sqrt{21}}\cdot\dfrac{\sqrt{21}}{\sqrt{3}+\sqrt{7}}=1\)
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\(\left(3\sqrt{5}+2\sqrt{6}+\sqrt{69}\right)\times\left(3\sqrt{5}+2\sqrt{6}-\sqrt{69}\right)\)
Tính
Tính
a. \(\sqrt{2}\left(\sqrt{21}+3\right)\sqrt{5-\sqrt{21}}\)
b. \(\sqrt{2}\left(\sqrt{5}-1\right)\sqrt{3+\sqrt{5}}\)
\(\left(\sqrt{3+\sqrt{5}}\right)\times\left(\sqrt{10}+\sqrt{2}\right)\times\left(3-\sqrt{5}\right)\)
Tính
\(=\frac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}.\left(\sqrt{10}+\sqrt{2}\right).\frac{6-2\sqrt{5}}{2}\)
\(=\frac{\sqrt{5}+1}{\sqrt{2}}.\sqrt{2}\left(\sqrt{5}+1\right).\frac{\left(\sqrt{5}-1\right)^2}{2}\)
\(=\frac{\left(\sqrt{5}+1\right)^2.\left(\sqrt{5}-1\right)^2}{2}\)
\(=\frac{\left[\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)\right]^2}{2}\)
\(=\frac{4^2}{2}=8\)
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Rút gọn:
Q = \(\frac{1}{2+\sqrt{3}}+\sqrt{3}-1+\sqrt{\left(3+2\sqrt{2}\right).\left(3-2\sqrt{2}\right)}\)
M = \(\left(5+\sqrt{21}\right).\left(\sqrt{14}-\sqrt{6}\right).\sqrt{5-\sqrt{21}}\)
N = \(\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{2}}-\sqrt{\sqrt{5}+1}\)
thực hiện phép tính:
\(\left(\sqrt{3}-2\right)\times\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
\(\sqrt{\frac{\sqrt{5}}{8\sqrt{5}+3\sqrt{35}}}\times\left(3\sqrt{2}+\sqrt{14}\right)\)