RÚT GỌN
X= \(\frac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\frac{\sqrt{2}-9\sqrt[3]{9}}{\sqrt[4]{2}-\sqrt[3]{81}}\)
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
\(x=\dfrac{3\sqrt[3]{8-3\sqrt{5}}}{\sqrt[3]{57}}.\sqrt[3]{8+3\sqrt{5}}=\dfrac{3\sqrt[3]{\left(8-3\sqrt{5}\right)\left(8+3\sqrt[]{5}\right)}}{\sqrt[3]{57}}=\sqrt[3]{\dfrac{19}{57}}=\dfrac{1}{\sqrt[3]{3}}\)
\(y=\dfrac{\left(\sqrt[3]{3}+\sqrt[4]{2}\right)\left(\sqrt[3]{3}-\sqrt[4]{2}\right)}{\sqrt[3]{3}+\sqrt[4]{2}}+\dfrac{\left(\sqrt[4]{2}-\sqrt[3]{81}\right)\left(\sqrt[4]{2}+\sqrt[3]{81}\right)}{\sqrt[4]{2}-\sqrt[3]{81}}\)
\(=\sqrt[3]{3}-\sqrt[4]{2}+\sqrt[4]{2}+\sqrt[3]{81}=\sqrt[3]{3}+3\sqrt[3]{3}=4\sqrt[3]{3}\)
\(T=xy=\dfrac{4\sqrt[3]{3}}{\sqrt[3]{3}}=4\)
\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)\(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\) Rút gọn biểu thức:a)\(\sqrt{4.36}+\sqrt{\frac{25}{81}\frac{16}{49}}\)
Rút gọn: A = \(\frac{a+\sqrt{2+\sqrt{5}}.\sqrt{\sqrt{9-4\sqrt{5}}}}{\sqrt[3]{2-\sqrt{5}}.\sqrt[3]{\sqrt{9-4\sqrt{5}}}-\sqrt[3]{a^2}+\sqrt[3]{a}}\)
Cho biểu thức: \(P=\left(\frac{\sqrt{x}-3}{2-\sqrt{x}}+\frac{\sqrt{x}+2}{3+\sqrt{x}}-\frac{9-x}{x+\sqrt{x}-6}\right):\left(1-\frac{3\sqrt{x}-9}{x-9}\right)\)
a)Rút gọn biểu thức
b)Tính P với \(x=\frac{\sqrt{4+2\sqrt{3}}\left(\sqrt{x}-1\right)}{\sqrt{6+2\sqrt{5}-\sqrt{5}}}\)
Mình ghi nhầm. \(x=\frac{\sqrt{4+2\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)nhé
Tính: \(B=\frac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\frac{\sqrt{2}-9\sqrt[3]{9}}{\sqrt[4]{2}-3\sqrt{81}}\)
Tính :
\(B=\frac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\frac{\sqrt{2}-9\sqrt[3]{9}}{\sqrt[4]{2}-3\sqrt{81}}\)
cho \(x=\frac{\sqrt[3]{5-3\sqrt{5}}+\sqrt[3]{64-12\sqrt{20}}}{\sqrt[3]{57}}.\)\(\sqrt[3]{8+3\sqrt{5}}\)
\(y=\frac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\frac{2-9\sqrt[3]{9}}{\sqrt[4]{2}-\sqrt{81}}\)
Tính xy
cho x=3√5−3√5+3√64−12√203√57 .3√8+3√5
y=3√9−√23√3+4√2 +2−93√94√2−√81
Tính xy
\(\text{Rút gọn biểu thức}\)
\(P=\sqrt{x}+\frac{\sqrt[3]{2-\sqrt{3}}.\sqrt[6]{7-4\sqrt{3}}-x}{\sqrt[4]{9-4\sqrt{5}}.\sqrt{2+\sqrt{5}}+\sqrt{x}}\)
mình nghĩ bài này sai đề,
ĐÚng phải là\(\sqrt[3]{2+\sqrt{3}}\)
( KHÔNG CHẮC NỮA :D )
Gía trị biểu thức A=\(\frac{\sqrt[3]{9}-\sqrt{2}}{\sqrt[3]{3}+\sqrt[4]{2}}+\frac{\sqrt{2}-9\sqrt[3]{9}}{\sqrt[4]{2}+\sqrt[3]{81}}\)là? (Làm tròn đến phần trăm sau dấu phẩy)