Volume of a cube is the product of its edges. In a cube, all the sides are of equal length. Hence, if one of the edges is known then the volume can be easily calculated. Volume of cube = \(side~\times~side~\times~side\)

\(125\)

\(\Rightarrow 5~\times~5~\times~5\)

\(\Rightarrow~a\)

Therefore the side of the cube is 5 units.

#### Methods for calculating the cube root of a number

Addition is the inverse of subtraction and multiplication is the inverse function of division. Similarly cube root is the inverse of a cube number. For example,

\(1^3\)

\(4^3\)

Please note that we will only consider the positive values cube roots of the natural numbers. We can write \(\sqrt[3]{125}\)

#### Prime Factorization

We can find the cube root of a number by the method of prime factorization . Consider the following example for a clear understanding:

\(2744\)

Therefore the cube root of \(2744\)

Illustration 1: Solve: \(\sqrt[3]{24389}\)

Solution: Prime factors = \(29~×~29~×~29\)

Therefore \(\sqrt[3]{24389}\)

Illustration 2: Find \(\sqrt[3]{46656}\)

Solution: Let us first find the prime factors:

\(46656\)

Therefore, \(\sqrt[3]{46656}\)

Learn more about the concept in depth through NCERT Solutions which is the latest edition from team Byju’s. Get detailed solutions to the questions of NCERT Books for chapter Cube and Cube Roots along with detailed explanation.

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