a) \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}\\ =3-\left(-2\right)-5\\ =3+2-5\\ =0\)
b) \(B=\sqrt[3]{7+5\sqrt{2}}\\ =\sqrt[3]{1+6+3\sqrt{2}+2\sqrt{2}}\\ =\sqrt[3]{1+3\sqrt{2}+6+2\sqrt{2}}\\ =\sqrt[3]{\left(1+\sqrt{2}\right)^2}\\ =1+\sqrt{2}\)
Thực hiện các phép tính sau :
a)A=\(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\) b)B=\(\left(2-\sqrt{3}\right).\sqrt[3]{26+15\sqrt{3}}\) c)C=\(\sqrt[3]{3+\sqrt{9+\dfrac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\dfrac{125}{7}}}\)
Tính
a) \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}\)
b) \(\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}.\sqrt[3]{4}\)
Rút gọn biểu thức sau:
a)M=\(3x-\sqrt[3]{27^3+27x^2+9x+1}\)
b)N=\(\sqrt[3]{8x^3+12x^2+6x+1}-\sqrt[3]{x^3}\)
1.Chứng minh:\(\dfrac{a+\sqrt{2+\sqrt{5}.}\sqrt{\sqrt{9-4\sqrt{5}}}}{3\sqrt{2-\sqrt{5}}.\sqrt[3]{\sqrt{9+4\sqrt{5}-}3\sqrt{a^2}+\sqrt[3]{a}}}\)=\(-\sqrt[3]{a}-1\)
2.Rút gọn: \(\left(\dfrac{a^3\sqrt[]{a}-2a^3\sqrt{b}+\sqrt[3]{a^2}-\sqrt[3]{b}}{\sqrt[3]{a^2-\sqrt[3]{ab}}}+\dfrac{\sqrt[3]{a^2b}-\sqrt[3]{ab^2}}{\sqrt[3]{a}-\sqrt[3]{b}}\right)1\dfrac{1}{\sqrt[3]{a^2}}\)
tính
a. \(\dfrac{\sqrt[3]{125}.\sqrt[3]{\dfrac{16}{10}}.\sqrt[3]{-0,5}}{\sqrt[3]{4}+\sqrt[3]{2}+1}\)
b.\(\sqrt[]{3+\sqrt[]{5}+\sqrt[]{10+6\sqrt[]{5}}}\)
Tính
a.A=\(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\)
b.B=\(\sqrt[3]{3+\sqrt{9+\dfrac{125}{7}}}-\sqrt[3]{-3+\sqrt{9+\dfrac{125}{7}}}\)
c.C=\(\sqrt[3]{26+15\sqrt{3}}.\left(2-\sqrt{3}\right)+\sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}}\)
A =\(\dfrac{x\sqrt[]{x}-3}{x-2\sqrt[]{x}-3}-\dfrac{2\left(\sqrt[]{x}-3\right)}{\sqrt[]{x}+1}+\dfrac{\sqrt[]{x}+3}{3-\sqrt[]{x}}\)
a. rút gọn A
b. Tính A với x = \(14-6\sqrt[]{5}\)
c. tìm min A
A=\(\dfrac{x\sqrt{x}-3}{x-2\sqrt{x}-3}-\dfrac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}+3}{3-\sqrt{x}}\)
a) Rút gọn A
b) Tính A với x=14-6\(\sqrt{5}\)
c) Tìm Min A
a) \(\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)
b) \(\dfrac{1}{\sqrt[3]{4-\sqrt{15}}}+\sqrt[3]{4-\sqrt{15}}\)
c) \(\dfrac{\sqrt[3]{a^4}+\sqrt[3]{a^2b^2}+\sqrt[3]{b^4}}{\sqrt[3]{a^2}+\sqrt[3]{ab}+\sqrt[3]{b^2}}\)
Rút gọn các biểu thức sau
