Rút gọn \(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
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30 tháng 5 2023 lúc 19:58
Rút gọn biểu thức
\(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}-3\sqrt{5\sqrt{48}}}\)
\(2\sqrt{5\sqrt{3}}-2\sqrt{8\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
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a: \(=2\sqrt{20\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\cdot\sqrt{20\sqrt{3}}\)
\(=4\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}\)
b: \(=2\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}\)
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Rút gọn biểu thức: \(\frac{\sqrt{20+8\sqrt{3}} +\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
cho x=\(\left(\dfrac{\sqrt[3]{8-3\sqrt{5}}+\sqrt[3]{64-12\sqrt{20}}}{\sqrt[3]{57}}\right)\sqrt[3]{8+3\sqrt{5}}\);y=\(\left(\dfrac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\dfrac{\sqrt{2}-9\sqrt[3]{9}}{\sqrt[4]{2}-\sqrt[3]{81}}\right)\)
a rút gọn x và y
b tính T = xy
\(x=\dfrac{3\sqrt[3]{8-3\sqrt{5}}}{\sqrt[3]{57}}.\sqrt[3]{8+3\sqrt{5}}=\dfrac{3\sqrt[3]{\left(8-3\sqrt{5}\right)\left(8+3\sqrt[]{5}\right)}}{\sqrt[3]{57}}=\sqrt[3]{\dfrac{19}{57}}=\dfrac{1}{\sqrt[3]{3}}\)
\(y=\dfrac{\left(\sqrt[3]{3}+\sqrt[4]{2}\right)\left(\sqrt[3]{3}-\sqrt[4]{2}\right)}{\sqrt[3]{3}+\sqrt[4]{2}}+\dfrac{\left(\sqrt[4]{2}-\sqrt[3]{81}\right)\left(\sqrt[4]{2}+\sqrt[3]{81}\right)}{\sqrt[4]{2}-\sqrt[3]{81}}\)
\(=\sqrt[3]{3}-\sqrt[4]{2}+\sqrt[4]{2}+\sqrt[3]{81}=\sqrt[3]{3}+3\sqrt[3]{3}=4\sqrt[3]{3}\)
\(T=xy=\dfrac{4\sqrt[3]{3}}{\sqrt[3]{3}}=4\)
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22 tháng 6 2023 lúc 16:47
Rút gọn biểu thứcI(2sqrt{3}-5sqrt{27}+4sqrt{12}):sqrt{3}Ksqrt{125}-4sqrt{45}+3sqrt{20}-sqrt{80}L2sqrt{9}+sqrt{25}-5sqrt{4}N2sqrt{32}-5sqrt{27}-4sqrt{8}+3sqrt{75}O2sqrt{3.5^2}-3sqrt{3.2^2}+sqrt{3.3^2}
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Rút gọn biểu thức
I=(2\(\sqrt{3}\)-5\(\sqrt{27}\)+4\(\sqrt{12}\)):\(\sqrt{3}\)
K=\(\sqrt{125}\)-4\(\sqrt{45}\)+3\(\sqrt{20}\)-\(\sqrt{80}\)
L=2\(\sqrt{9}\)+\(\sqrt{25}\)-5\(\sqrt{4}\)
N=2\(\sqrt{32}\)-5\(\sqrt{27}\)-4\(\sqrt{8}\)+3\(\sqrt{75}\)
O=2\(\sqrt{3.5^2}\)-3\(\sqrt{3.2^2}\)+\(\sqrt{3.3^2}\)
\(I=\left(2\sqrt{3}-5\sqrt{27}+4\sqrt{12}\right):\sqrt{3}\)
\(=\left(2\sqrt{3}-5\sqrt{3}.\sqrt{3^2}+2\sqrt{2^2}.\sqrt{3}\right):\sqrt{3}\)
\(=\left(2\sqrt{3}-15\sqrt{3}+8\sqrt{3}\right):\sqrt{3}\)
\(=-5\sqrt{3}.\dfrac{1}{\sqrt{3}}\)
\(=-5\)
\(K=\sqrt{125}-4\sqrt{45}+3\sqrt{20}-\sqrt{80}\)
\(=\sqrt{5^2.5}-4\sqrt{3^2.5}+3\sqrt{2^2.5}-\sqrt{4^2.5}\)
\(=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}\)
\(=\sqrt{5}.\left(5-12+6-4\right)\)
\(=-5\sqrt{5}\)
\(L=2\sqrt{9}+\sqrt{25}-5\sqrt{4}\)
\(=2\sqrt{3^2}+\sqrt{5^2}-5\sqrt{2^2}\)
\(=2.3+5-5.2\)
\(=1\)
\(N=2\sqrt{32}-5\sqrt{27}-4\sqrt{8}+3\sqrt{75}\)
\(=2.4\sqrt{2}-5.3\sqrt{3}-4.2\sqrt{2}+3.5\sqrt{3}\)
\(=8\sqrt{2}-8\sqrt{2}-15\sqrt{3}+15\sqrt{3}\)
\(=0\)
\(O=2\sqrt{3.5^2}-3\sqrt{3.2^2}+\sqrt{3.3^2}\)
\(=2.5\sqrt{3}-3.2\sqrt{3}+3\sqrt{3}\)
\(=10\sqrt{3}-6\sqrt{3}+3\sqrt{3}\)
\(=7\sqrt{3}\)
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\(L=\dfrac{2\sqrt{3}-15\sqrt{3}+8\sqrt{3}}{\sqrt{3}}=2-15+8=-5\)
\(K=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}=-5\sqrt{5}\)
L=2*3+5-5*2=5-4=1
N=8căn 2-8căn2-15căn3+15căn 3=0
O=10căn 3-6căn3+3căn3=7căn 3
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Rút gọn
\(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
\(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
Thực hiện phép tính rút gọn sau:
\(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}-\dfrac{\sqrt{5}-5}{\sqrt{5}}\)
\(C=\dfrac{1}{\sqrt{3}+\sqrt{2}}+\sqrt{7-4\sqrt{3}}+\sqrt{2}\)
a: Ta có: \(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(=2\sqrt{2}-6\sqrt{2}+15\sqrt{2}\)
\(=11\sqrt{2}\)
b: Ta có: \(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}+\dfrac{5-\sqrt{5}}{\sqrt{5}}\)
\(=5\sqrt{5}-\sqrt{5}+\sqrt{5}-1\)
\(=5\sqrt{5}-1\)
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25 tháng 12 2023 lúc 14:34
1) Rút gọn các biểu thức sau:a) sqrt[3]{27} - sqrt[3]{-8} - sqrt[3]{125}b) sqrt{20} - sqrt{45} + 3sqrt{18} + sqrt{72}c) 2sqrt{5} + sqrt{left(1-sqrt{5}right)^2} d) dfrac{1}{sqrt{3}+1} + dfrac{1}{sqrt{3}-1} - 2sqrt{3}e) dfrac{a-b}{sqrt{a}-sqrt{b}} - dfrac{sqrt{a^3}-sqrt{b^3}}{a-b} với a ≥ 0 , b≥0 , a ≠ b
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1) Rút gọn các biểu thức sau:
a) \(\sqrt[3]{27}\) - \(\sqrt[3]{-8}\) - \(\sqrt[3]{125}\)
b) \(\sqrt{20}\) - \(\sqrt{45}\) + 3\(\sqrt{18}\) + \(\sqrt{72}\)
c) 2\(\sqrt{5}\) + \(\sqrt{\left(1-\sqrt{5}\right)^2}\)
d) \(\dfrac{1}{\sqrt{3}+1}\) + \(\dfrac{1}{\sqrt{3}-1}\) - 2\(\sqrt{3}\)
e) \(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\) - \(\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\) với a ≥ 0 , b≥0 , a ≠ b
Rút gọn biểu thức \(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
=\(16\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}\)=\(16\sqrt{2\sqrt{3}}-8\sqrt{5\sqrt{3}}\)
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Rút gọn \(A=\left(\sqrt{6+\sqrt{20}}-2\sqrt{3-\sqrt{5}}+\sqrt{15-10\sqrt{2}}\right):\left(2+\sqrt{8}\right)\)
\(A=\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{2}.\sqrt{6-2\sqrt{5}}+\sqrt{\left(\sqrt{10}-\sqrt{5}\right)^2}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{5}+1-\sqrt{2}\left(\sqrt{5}-1\right)+\sqrt{10}-\sqrt{5}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{5}+1-\sqrt{10}+\sqrt{2}+\sqrt{10}-\sqrt{5}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{2}+1}{2\left(\sqrt{2}+1\right)}=\dfrac{1}{2}\)
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