Find the cube root of 35937 by using
a) prime factorization method

Given: The number is 35937

To do: Find the cube root of 35937 by using prime factorization method

Answer:

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 35937 by prime factorization method:

The prime factorization of a number is the product of all its prime factors.

$35937 = 3 \times 3 \times 3 \times 11 \times 11 \times 11$

$∛35937 = ∛(3 \times 3 \times 3 \times 11 \times 11 \times 11) = 3 \times 11 = 33$

Therefore, $∛35937 = 33$