Question

Cube root of 175616 by prime factorization method

Answer 1

So 56 is the cube root...

Answer 2

Cube root of 175616 by prime factorization method is 56

Solution:

To find cube root of 175616 by prime factorization method

A number that must be multiplied by 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 175616:

$\text{ prime factors of 175616 } = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7$

Thus we get,

$\sqrt[3]{175616} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7}$

Make the groups of 3 of equal numbers

$\sqrt[3]{175616} = \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{2 \times 2 \times 2 \times } \times \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{7 \times 7 \times 7}$

So there are 4 equal groups. So from that group take one factor out

$\sqrt[3]{175616} = 2 \times 2 \times 2 \times 7 = 56$

Thus Cube root of 175616 by prime factorization method is 56

Learn more about Cube root of 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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