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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