Cube Roots

Three numbers are in the ratio $2:3:4$. If the sum of their cubes is $50,688$, then find each number. 

The sum of two perfect cubes is $854$. If the cube root of smaller number is $5$, then find the cube root of the larger number.

A decimal number is multiplied by its square. If the product so obtained is $614.125$, find the decimal number.

If $n^3=4\frac{12}{125}$, then find the value of $n^2-1$.

The sum of the cubes of three numbers is in the ratio $1:3:4$ is $17576$. Find the numbers.

Find the edge of a cube whose volume is $166.375 {\mathrm{cm}}^3$.

Find the smallest number by which $140625$ must be divided, so that the quotient thus obtained is a perfect cube. Also find the cube root of the number thus obtained.

Find the value of the following:

$\sqrt[3]{\frac{5832}{6859}}$

Find the value of the following:

$\sqrt[3]{274.625}$

Find the value of the following:

$\sqrt[3]{1125\times 1944}$

Find the value of the following:

$\sqrt[3]{125\times 64}$

Find the cube root of the following number by using prime factorisation.

$15625$

Find the cube root of the following number by using prime factorisation.

$6859$

Find the cube root of the following number by using prime factorisation.

$5832$

Find the cube root of the following number by using prime factorisation.

$2197$

Find the cube root of the following number by finding its ones and tens digit.

$12167$

Find the cube root of the following number by finding its ones and tens digit.

$4096$

Find the cube root of the following number by finding its ones and tens digit.

$729$

Find the cube root of the following number by finding its ones and tens digit.

$3375$

Find the edge of the cubical box if its volume is $110.592 {\mathrm{m}}^3$.