Question

Answer 1

a: \(\sqrt[3]{27}-\sqrt[3]{-8}+\frac15\cdot\sqrt[3]{-125}\)

\(=3-\left(-2\right)+\frac15\cdot\left(-5\right)\)

=3+2-1

=5-1

=4

b: \(\sqrt[3]{\frac{125}{512}}+\sqrt[3]{125}-\frac13\cdot\sqrt{27}\)

\(=\frac58+5-\frac13\cdot3\sqrt3=\frac{45}{8}-\sqrt3\)

c: \(\sqrt[3]{x^3+3x^2+3x+1}\)

\(=\sqrt[3]{\left(x+1\right)^3}\)

=x+1

d: \(\sqrt[3]{8x^3+12x^2+6x+1}\)

\(=\sqrt[3]{\left.\left(2x+1\right)^3\right.}\)

=2x+1