Question

find the cube root of 729 by prime factorization method

Answer 1

Factorize 729 first...

729=3*3*3*3*3*3

$\sqrt[3]{729} = \sqrt[3]{3 \times 3 \times 3 \times 3 \times 3 \times 3}$
$\sqrt[3]{729} = 9$

So, 9 is the cube root of 729

Answer 2

Cube root of 729 by prime factorization method is 9

Solution:

To find cube root of 729 by prime factorization method

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

Prime factorization method:

Prime factorization is a number written as the product of all its prime factors.

In order of finding cube root by prime factorization we use the following steps:

Step I : Obtain the given number

Step II : Resolve it into prime 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

Prime factorization of 729:

$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$

$\sqrt[3]{729} = \sqrt[3]{3 \times 3 \times 3 \times 3 \times 3 \times 3}$

Make the groups of 3 of equal numbers. There are two groups, so from each group take one factor

$\sqrt[3]{729}=\sqrt[3]{3 \times 3 \times 3}\times\sqrt[3]{3 \times 3 \times 3}$

$\sqrt[3]{729} = 3 \times 3 = 9$

Thus cube root of 729 by prime factorization method is 9

Learn more about cube roots and prime factorization

1) Find the cube roots of the following numbers: (i) -5832

2) Find the cube root of each of the following: (i) -216 x 1728

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Find the cube root of the following numbers by prime factorization method.

(i) 343

(ii) 729

(iii) 1331

(iv) 2744

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