rút gọn các biểu thức: C= \(\frac{2}{3}\)\(\sqrt{144}\)-\(\left(-\frac{3}{4}\right)\): \(\sqrt{\frac{225}{144}}\)
D=\(\frac{4^6.25^5-2^{12}.25^4}{2^{12}.5^8-10^8.64}\)
Những câu hỏi liên quan
Thực hiện phép tính sau
a. F=[12(1)-2,3(6)]:4,(21)
b.\(\frac{1\frac{11}{34}.4\frac{3}{7}-\left(\frac{3}{2}-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}.\left(12-5\frac{1}{3}\right)}\)
c.1-\(\frac{\sqrt{121}}{\sqrt{196}}-\frac{\sqrt{169}}{\sqrt{144}}+\frac{\sqrt{25}}{\sqrt{36}}+\left(-1\frac{2}{3}\right):\left(-3\frac{1}{3}\right)\)
Minh AnNgọc HnueBăng Băng 2k6Thảo PHồ Đđề bài khó wáỖ CHÍ DŨNGBảo TrâmhLương Minh HằngươngAnh Qua
c/
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{-5}{3}:\frac{-10}{3}\)
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{-5}{3}.\frac{-3}{10}\)
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{1}{2}\)
\(=1-\left(\frac{66}{84}+\frac{98}{84}-\frac{70}{84}-\frac{42}{84}\right)\)
Mik làm tiếp nhé tại lúc nãy bấm nhầm!
Câu c/ (tiếp theo)
\(=1-\frac{52}{84}\)
\(=\frac{84}{84}-\frac{52}{84}=\frac{32}{84}=\frac{8}{21}\)
Câu a: Sai đề
rút gọn biểu thức N= \(12\left(\sqrt{2}-3\sqrt{18}+212\sqrt{8}\right):\sqrt{2}\)
N=\(\frac{5-\sqrt{5}}{\sqrt{5-1}}-\frac{4}{\sqrt{5+1}}\)
Tính:
1) left(sqrt{45}-sqrt{20}+sqrt{5}right):sqrt{6}
2) frac{sqrt{10}-sqrt{15}}{sqrt{8}-sqrt{12}}
3) frac{1}{3+sqrt{2}}+frac{1}{3-sqrt{2}}
4) sqrt{3}left(sqrt{12}+sqrt{27}-sqrt{3}right)
5) sqrt{144}-sqrt{25}.sqrt{4}
6) frac{1}{sqrt{3}-1}-sqrt{3}+1
Đọc tiếp
Tính:
1) \(\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
2) \(\frac{\sqrt{10}-\sqrt{15}}{\sqrt{8}-\sqrt{12}}\)
3) \(\frac{1}{3+\sqrt{2}}+\frac{1}{3-\sqrt{2}}\)
4) \(\sqrt{3}\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)\)
5) \(\sqrt{144}-\sqrt{25}.\sqrt{4}\)
6) \(\frac{1}{\sqrt{3}-1}-\sqrt{3}+1\)
\(1,\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(\sqrt{9.5}\sqrt{4.5}+\sqrt{5}\right).\frac{1}{\sqrt{6}}\)
\(=\frac{2\sqrt{5}}{\sqrt{6}}\)
\(=\frac{\sqrt{30}}{3}\)
1) \(\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(\sqrt{9.5}-\sqrt{4.5}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(3\sqrt{5}-2\sqrt{5}+\sqrt{5}\right):\sqrt{6}\)
\(=\frac{2\sqrt{5}}{\sqrt{6}}\)
\(=\frac{2\sqrt{5}\sqrt{6}}{\sqrt{6}.\sqrt{6}}\)
\(=\frac{2\sqrt{30}}{6}\)
\(=\frac{\sqrt{30}}{3}\)
SGK Chân trời sáng tạo
20 tháng 8 2023 lúc 19:43
Rút gọn biểu thức \({\left[ {{{\left( {\frac{1}{3}} \right)}^2}} \right]^{\frac{1}{4}}}.{\left( {\sqrt 3 } \right)^5}\), ta được
A. \(\sqrt 3 \).
B. \(3\sqrt 3 \).
C. \(\frac{1}{{\sqrt 3 }}\).
D. 9.
\({\left[ {{{\left( {\frac{1}{3}} \right)}^2}} \right]^{\frac{1}{4}}}.{\left( {\sqrt 3 } \right)^5} = {\left( {\frac{1}{3}} \right)^{2.\frac{1}{4}}}.{\left( {{3^{\frac{1}{2}}}} \right)^5} = {\left( {{3^{ - 1}}} \right)^{\frac{1}{2}}}{.3^{\frac{1}{2}.5}} = {3^{ - \frac{1}{2}}}{.3^{\frac{5}{2}}} = {3^{ - \frac{1}{2} + \frac{5}{2}}} = {3^2} = 9\)
Chọn D.
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Rút gọn các biểu thức sau:
a.\(\sqrt{5.\left(1-2\right)^2}\)
b.\(\sqrt{27.\left(2-\sqrt{5}\right)^2}\)
c.\(\sqrt{\frac{2}{\left(3-10\right)^2}}\)
d.\(\sqrt{\frac{5.\left(1-\sqrt{3}\right)^2}{4}}\)
e.\(\sqrt{\frac{4}{9-4\sqrt{5}}}+\sqrt{\frac{9}{9+4\sqrt{5}}}\)
Bài 1: Rút gọn biểu thức1) sqrt{12}-sqrt{27}+sqrt{48} 2) left(sqrt{25}+sqrt{20}-sqrt{80}right):sqrt{5}3) 2sqrt{27}-sqrt{frac{16}{3}}-sqrt{48}-sqrt{8frac{1}{3}} 4) frac{1}{sqrt{5}-sqrt{3}}-frac{1}{sqrt{5}+sqrt{3}}5) left(sqrt{125}-sqrt{12}-2sqrt{5}right)left(3sqrt{5}-sqrt{3}+sqrt{27}right) 6) left(3sqrt{20}-sqrt{125}-15sqrt{frac{1}{5}}right).sqrt{5}7) left(6sqrt{128}-frac{3}{5}sqrt{50}+7sqrt{8}right):3sqrt{2} 8) left(2sqrt{48}-frac{3}{2}sqrt{frac{4}{3}}+sqrt{27}right).2sqrt{3...
Đọc tiếp
Bài 1: Rút gọn biểu thức
1) \(\sqrt{12}-\sqrt{27}+\sqrt{48}\) 2) \(\left(\sqrt{25}+\sqrt{20}-\sqrt{80}\right):\sqrt{5}\)
3) \(2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\) 4) \(\frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{5}+\sqrt{3}}\)
5) \(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\) 6) \(\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}\)
7) \(\left(6\sqrt{128}-\frac{3}{5}\sqrt{50}+7\sqrt{8}\right):3\sqrt{2}\) 8) \(\left(2\sqrt{48}-\frac{3}{2}\sqrt{\frac{4}{3}}+\sqrt{27}\right).2\sqrt{3}\)
9) \(\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{8}-4\right)^2}\) 10) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{\left(\sqrt{15}-3\right)^2}\)
11) \(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\) 12) \(\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
13) \(\sqrt{15-6\sqrt{6}}\) 14) \(\sqrt{8-2\sqrt{15}}\) 15) \(\sqrt[3]{-2}.\sqrt[3]{32}+\sqrt{2}.\sqrt{32}\)
Rút gọn biểu thức:
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^4.14^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^4.2^3.7^3}\)
\(=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^4.7^3\left(5^5+2^3\right)}\)
\(=\frac{1}{6}+\frac{93750}{3133}\)
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Rút gọn các biểu thức
\(B=\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}} \)
\(C=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(D=\frac{3\sqrt{8}-2\sqrt{12}+20}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
\(B=\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}=\frac{9\sqrt{5}+9\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{9\left(\sqrt{5}+\sqrt{3}\right)}{\sqrt{5}+\sqrt{3}}=9\)
\(C=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\sqrt{2}+1\)
mik chỉnh lại đề
\(D=\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}=\frac{6\sqrt{2}-4\sqrt{3}+2\sqrt{5}}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}\)
\(=\frac{2\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}{3\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}=\frac{2}{3}\)
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cho biểu thức M=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(\frac{3\sqrt{x}-5}{\sqrt{x}-2}+\frac{2\sqrt{x}+10}{x+6\sqrt{x}+5}\right)\)
Rút gọn