Question

cube root of 343 by prime factorization method

Answer 1

7 is the Cube of 343

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Answer 2

Cube root of 343 by prime factorization method is 7

Solution:

To find cube root of 343 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 343:

The prime factors of 343 = 7 x 7 x 7

$\sqrt[3]{343} = \sqrt[3]{7 \times 7 \times 7}$

Make the groups of 3 of equal numbers. There are 1 groups, so from that group take one factor out

$\sqrt[3]{343} = 7$

Thus cube root of 343 by prime factorization is 7

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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