Find the Cube root of 7056 by prime factorization method.

Given :

The given number is 7056

To find :

We have to find the cube root of 7056 by prime factorization.

Solution :

A number that must be multiplied by itself three times to equal a given number is called cube root.

Step I : Obtain the given number

Step II : Resolve it into factors.

Step III : Group the factors in 3 in such a way that each number of the group is same

Step IV : Take one factor from each group

Step V : Find the product of the factors obtained in step IV. This product is the required cube root

Finding the cube root of 7056 by prime factorization method:

The prime factorization of a number is the product of all its prime factors.

$7056 = 2\times2\times2\times2\times3\times3\times7\times7$

$\displaystyle \sqrt[3]{7056} \ =\ \sqrt[3]{2\times 2\times 2\times 2\times 3\times 3\times 7\times 7}$

            $= 2\sqrt[3]{2\times 3\times 3\times 7\times 7}$

             $\displaystyle =2\sqrt[3]{882}$

             $=2 \times 9.59$

             $= 19.18$

Cube root of 7056 is 19.18