\(\sqrt{\dfrac{8+\sqrt{15}}{2}+\dfrac{8-\sqrt{15}}{2}}=\sqrt{\dfrac{16}{2}}=\sqrt{8}=2\sqrt{2}\)
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Chương I - Căn bậc hai. Căn bậc ba
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29 tháng 6 2021 lúc 9:04
* Rút gọn biểu thức
c.\(\dfrac{1}{2\sqrt{2}}-\dfrac{3}{2}\sqrt{4,5}+\dfrac{2}{5}\sqrt{50}\)
d.\(\dfrac{4}{3+\sqrt{5}}-\dfrac{8}{1+\sqrt{5}}+\dfrac{15}{\sqrt{5}}\)
Tính:a. 5sqrt{2}-2sqrt{48}+6sqrt{75}-sqrt{108}b.2sqrt{147}-dfrac{3}{32}sqrt{192}+dfrac{4}{18}sqrt{243}-dfrac{1}{10}sqrt{300}c. -dfrac{1}{2}sqrt{108}+dfrac{1}{15}sqrt{75}-dfrac{1}{22}sqrt{363}+sqrt{12} d. dfrac{5}{8}sqrt{48}-dfrac{1}{33}sqrt{363}+dfrac{3}{14}sqrt{147}-dfrac{1}{4}sqrt{192}e. dfrac{3}{2}sqrt{12}+dfrac{7}{5}sqrt{75}-dfrac{9}{10}sqrt{300}+dfrac{11}{6}sqrt{108}
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Tính:
a. \(5\sqrt{2}-2\sqrt{48}+6\sqrt{75}-\sqrt{108}\)
b.\(2\sqrt{147}-\dfrac{3}{32}\sqrt{192}+\dfrac{4}{18}\sqrt{243}-\dfrac{1}{10}\sqrt{300}\)
c. \(-\dfrac{1}{2}\sqrt{108}+\dfrac{1}{15}\sqrt{75}-\dfrac{1}{22}\sqrt{363}+\sqrt{12}\)
d. \(\dfrac{5}{8}\sqrt{48}-\dfrac{1}{33}\sqrt{363}+\dfrac{3}{14}\sqrt{147}-\dfrac{1}{4}\sqrt{192}\)
e. \(\dfrac{3}{2}\sqrt{12}+\dfrac{7}{5}\sqrt{75}-\dfrac{9}{10}\sqrt{300}+\dfrac{11}{6}\sqrt{108}\)
Tính
\(A=\sqrt{20}-3\sqrt{8}+5\sqrt{45}\)
\(B=\dfrac{30}{\sqrt{7}-1}+\dfrac{15}{\sqrt{7}+2}\)
\(C=\left(3-\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\right)\left(3+\dfrac{5+\sqrt{5}}{\sqrt{5}+1}\right)\)
\(D=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(E=\sqrt{7-4\sqrt{3}}-\sqrt{3+2\sqrt{3}}\)
\(A=\dfrac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}+2\sqrt{2}\\ B=\left(5+2\sqrt{6}\right)\cdot\left(49-20\sqrt{6}\right)\cdot\sqrt{5-2\sqrt{6}}\)
\(C=\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
\(D=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}+\dfrac{1}{4}\sqrt{8}\right)\cdot3\sqrt{6}\)
Thực hiện phép tính
a, \(\sqrt{18}-\dfrac{1}{2}\sqrt{48}-\sqrt{8}+\dfrac{4-5\sqrt{2}}{5-2\sqrt{2}}\)
b, \(\dfrac{\sqrt{15}-2\sqrt{3}}{2-\sqrt{5}}+6\sqrt{\dfrac{1}{3}}+\dfrac{13}{\sqrt{3}-4}\)
\(\dfrac{8\sqrt{x}-x-31}{x-8\sqrt{x}-15}-\dfrac{\sqrt{x}+5}{\sqrt{x}-3}-\dfrac{3\sqrt{x}-1}{5-\sqrt{x}}\) rút gọn giùm ae
bà 1 rút gọn biểu thức :sqrt{9ab} + 7sqrt{dfrac{a}{b}} - 5sqrt{dfrac{b}{a}} - 3ab sqrt{dfrac{1}{ab}}bài 2 :cho a0,b0 chứng minh : dfrac{a^2b}{a-b}.sqrt{dfrac{8left(a^2-2ab+b^2right)}{75a^4b}} dfrac{2}{15} .sqrt{6b}
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bà 1 rút gọn biểu thức :\(\sqrt{9ab}\) + 7\(\sqrt{\dfrac{a}{b}}\) - 5\(\sqrt{\dfrac{b}{a}}\) - 3ab \(\sqrt{\dfrac{1}{ab}}\)
bài 2 :cho a>0,b>0 chứng minh : \(\dfrac{a^2b}{a-b}\).\(\sqrt{\dfrac{8\left(a^2-2ab+b^2\right)}{75a^4b}}\) = \(\dfrac{2}{15}\) .\(\sqrt{6b}\)
Rút gọn
a) 2sqrt{5}-sqrt{125}-sqrt{80}+sqrt{605}
b) dfrac{10+2sqrt{10}}{sqrt{5}+sqrt{2}}+dfrac{8}{1-sqrt{5}}
c) sqrt{15-sqrt{216}}+sqrt{33-12sqrt{6}}
d) dfrac{2sqrt{8}-sqrt{12}}{sqrt{18}-sqrt{48}}-dfrac{sqrt{5}+sqrt{27}}{sqrt{30}+sqrt{162}}
e) 2sqrt{dfrac{16}{3}}-3sqrt{dfrac{1}{27}}-6sqrt{dfrac{4}{75}}
Đọc tiếp
Rút gọn
a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
b) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
c) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
d) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
e) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
\(C=\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
\(B=\dfrac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)