Cube Roots

Three numbers are in the ratio $2:3:4.$ The sum of their cubes is $0.334125.$ Find the numbers.

Three numbers are in the ratio $1:2:3$ and the sum of their cubes is $4500$. Find the numbers.

Find the length of each side of a cube if its volume is $512 {\mathrm{cm}}^3$.

By what smallest number should $3600$ be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

Using prime factorisation, find the cube roots of $2197$

Using prime factorisation, find the cube roots of $512$

Using prime factorisation, find if the number $1331$ is a perfect cube or not. 

Using prime factorisation, find if the number $729$ is a perfect cube or not. 

Using prime factorisation, find if the number $343$ is a perfect cube or not. 

Using prime factorisation, find if the number $128$ is a perfect cube or not. 

Show that $500$ is not a perfect square.

$\sqrt[3]{8+27}=\sqrt[3]{8}+\sqrt[3]{27}$

There is no cube root of a negative integer.

Cube roots of $8$ are $+2$ and $–2$.

$363\times 81$ is a perfect cube.

$999$ is a perfect cube.

The least number by which$72$ be divided to make it a perfect cube is _____ .

The least number by which$72$ be multiplied to make it a perfect cube is _____ .

The cube root of a number $x$ is denoted by $x^{\frac{1}{k}}$, then the value of $k$ is _____ .

Evaluate: $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$