Ta có:

+ 3√512=3√83=8;5123=833=8;

+ 3√−729=3√(−9)3=−9;−7293=(−9)33=−9;

+ 3√0,064=3√0,43=0,4;0,0643=0,433=0,4;

+ 3√−0,216=3√(−0,6)3=−0,6;−0,2163=(−0,6)33=−0,6;

+ 3√−0,008=3√(−0,2)3=−0,2.

Đáp án:

( lần lượt như trên nhé!!! Ko viết lại đề)

8 ; - 9 ; 0,4 ; - 0,6 ; - 0,2

Kết quả lần lượt là $8$ ; $-9$ ; $0,4$ ; $-0,6$ ; $-0,2$

a) Ta có: \(-3\sqrt{16}\cdot\sqrt{90}\)

\(=-3\cdot4\cdot3\sqrt{10}\)

\(=-36\sqrt{10}\)

b) Ta có: \(3\sqrt{\dfrac{4}{3}}-3\sqrt{48}+5\sqrt{75}\)

\(=3\cdot\dfrac{2}{\sqrt{3}}-3\cdot4\sqrt{3}+5\cdot5\sqrt{3}\)

\(=2\sqrt{3}-12\sqrt{3}+25\sqrt{3}\)

\(=15\sqrt{3}\)

c) Ta có: \(4\sqrt[3]{27}-\sqrt[3]{64}-2\sqrt[3]{8}\)

\(=4\cdot3-4-2\cdot2\)

\(=12-4-4=4\)

\(x=\dfrac{3\sqrt[3]{8-3\sqrt{5}}}{\sqrt[3]{57}}.\sqrt[3]{8+3\sqrt{5}}=\dfrac{3\sqrt[3]{\left(8-3\sqrt{5}\right)\left(8+3\sqrt[]{5}\right)}}{\sqrt[3]{57}}=\sqrt[3]{\dfrac{19}{57}}=\dfrac{1}{\sqrt[3]{3}}\)

\(y=\dfrac{\left(\sqrt[3]{3}+\sqrt[4]{2}\right)\left(\sqrt[3]{3}-\sqrt[4]{2}\right)}{\sqrt[3]{3}+\sqrt[4]{2}}+\dfrac{\left(\sqrt[4]{2}-\sqrt[3]{81}\right)\left(\sqrt[4]{2}+\sqrt[3]{81}\right)}{\sqrt[4]{2}-\sqrt[3]{81}}\)

\(=\sqrt[3]{3}-\sqrt[4]{2}+\sqrt[4]{2}+\sqrt[3]{81}=\sqrt[3]{3}+3\sqrt[3]{3}=4\sqrt[3]{3}\)

\(T=xy=\dfrac{4\sqrt[3]{3}}{\sqrt[3]{3}}=4\)

a: Sửa đề: căn 6+2căn 5-căn 5

\(a=\dfrac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{\sqrt{5}+1-\sqrt{5}}=\dfrac{2}{1}=2\)

b: \(a^3=2-\sqrt{3}+2+\sqrt{3}+3a\)

=>a^3-3a-4=0

=>a^3-3a=4

\(\dfrac{64}{\left(a^2-3\right)^3}-3a=\left(\dfrac{4}{a^2-3}\right)^3-3a\)

\(=\left(\dfrac{a^3-3a}{a^2-3}\right)^3-3a=a^3-3a\)

=4

b: Ta có: \(\sqrt[3]{-0.008}-\dfrac{1}{5}\cdot\sqrt[3]{64}+5\cdot\sqrt[3]{\left(-5\right)^3}\)

\(=-\dfrac{1}{5}-\dfrac{1}{5}\cdot4+5\cdot\left(-5\right)\)

\(=-\dfrac{1}{5}-\dfrac{4}{5}-25\)

=-26

\(a.\sqrt{72}-5\sqrt{2}+3\sqrt{12}\\ =6\sqrt{2}-5\sqrt{2}+6\sqrt{3}\\ =\sqrt{2}+6\sqrt{3}\\ b.6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-5\sqrt{2}\\ =3\sqrt{2}-\sqrt{2}-5\sqrt{2}\\ =-3\sqrt{2}\\ c.\dfrac{\sqrt{8}-2}{\sqrt{2}-1}+\dfrac{2}{\sqrt{3}-1}-\dfrac{3}{\sqrt{3}}\\ =2+1+\sqrt{3}-\sqrt{3}\\ =3\\ d.\sqrt[3]{64}+\sqrt[3]{27}-2\sqrt[3]{-8}\\ =4+3+4\\ =11\)

= 5+(-7) - 2.4 - \(\dfrac{1}{3}\).6

= - 12