Question

The cube root of 35937 is
A) 33
B) 45
C) 27
D) 31

Answer 1

Hint:
Here, we will first find the prime factorization of the given number by computing the lowest common multiple, LCM and then find the cube root from the obtained prime factors. Then the obtained number will be the cube root.

Complete step by step solution:
We are given that the number is 35937.
We know that the prime factorization is finding which prime number multiply together to make the original number.
We will now find the prime factorization of 35937 from the given number.

Thus, we have the prime factorization of the number 35937 is \[3 \times 3 \times 3 \times 11 \times 11 \times 11\].
Finding the cube root of the number 35937 using the above prime factors, we get
\[
   \Rightarrow \sqrt[3]{{35937}} = \sqrt[3]{{3 \times 3 \times 3 \times 11 \times 11 \times 11}} \\
   \Rightarrow \sqrt[3]{{35937}} = \sqrt[3]{{{3^3} \times {{11}^3}}} \\
   \Rightarrow \sqrt[3]{{35937}} = 3 \times 11 \\
   \Rightarrow \sqrt[3]{{35937}} = 33 \\
 \]

Therefore, the cube root of 35937 is 33.

Note:
In solving these types of questions, you should know that the prime factorization means finding the prime number, which gets multiplied together to form the original number. First, we need to remember that finding the LCM is the easiest way to find the factors. Do not try to find the cube root directly by assuming or else the final answer can be wrong.