Find the cube root of 1404928.

Given :

The given number is 1404928.

To do :

We have to find the cube root of the given number.

Solution :

A cube of a number is a product obtained by multiplying the number with itself three times.

For example, the cube of $a = a \times a \times a = a^3$

The cube root of a number can be found by the prime factorization method.

Prime factorisation of 1404928 is,

2	1404928
2	2 $\times$ 702464
2	2$\times$ 2$\times$351232
2	2$\times$ 2$\times$ 2$\times$ 175616
2	2$\times$2$\times$2$\times$2$\times$87808
2	2$\times$2$\times$2$\times$2$\times$2$\times$43904
2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$ 21952
2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$ 10976
2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$5488
2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2744

2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$1372
2	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$686
7	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$343
7	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$7$\times$49
7	2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$7$\times$7$\times$7

Prime factorisation of $1404928 = (2\times2\times2)\times(2\times2\times2)\times(2\times2\times2)\times(2\times2\times2)\times(7\times7\times7)$

Therefore, cube root of $1404928 = 2\times2\times2\times2\times7 = 16\times7 =112$.

Therefore, the cube root of 1404928 is 112.

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Updated on: 10-Oct-2022

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