find the cube root of 35937by using prime factorization method
Answers
Answer:
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}
3
35937
=
3
3×3×3×11×11×11
Make the groups of 3 of equal numbers and from that group take one factor out
\begin{gathered}\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\end{gathered}
3
35937
=
3
3×3×3
×
3
11×11×11
3
35937
=3×11=33
Thus cube root of 35937 by using prime factorization method is 33
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Answer:
Thus, we have the prime factorization of the number 35937 is 3×3×3×11×11×11. Therefore, the cube root of 35937 is 33