Question

find the cube root of 35937 by using prime factorization method, without finding prime factors

Answer 1

Hey frnd
Here is your answer pls refer to the attachment
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Answer 2

Cube root of 35937 by prime factorization method is 33

Solution:

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 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

Cube root by Prime factorization of 35937

$\sqrt[3]{35937} = \sqrt[3]{3 \times 3 \times 3 \times 11 \times 11 \times 11}$

Make the groups of 3 of equal numbers and from that group take one factor out

$\sqrt[3]{35937} = \sqrt[3]{3 \times 3 \times 3} \times \sqrt[3]{11 \times 11 \times 11}\\\\\sqrt[3]{35937} = 3 \times 11 = 33$

Thus cube root of 35937 by using prime factorization method is 33

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