The cube root of 5832 is ____.

Question

Infinity Learn · Accepted Answer

Concept- The cube root of 5832 is 18. Here, it is important to first understand what a cube root is. Then, we can use the prime factorization approach, particularly the division method, to find the cube root. Only prime numbers may be used for division, and the division process must be continued until the quotient is 1. Group the identical numbers in a group of three after prime factorization. To obtain the necessary cube root, multiply one element from each group.
In this case, we must determine the cube root of

5832 .

We are aware that a number's cube root is a unique value that, when multiplied three times, results in the given number. That is, we can write x = a

\times

a

\times

a if "a" is

the cube root of x . For instance, cube of 2 = 2 \times 2 \times 2 = 8, therefore 8 has a cube root of 3 .

The prime factorization method can be used in this case to determine the cube root.
We factorize the numbers into prime numbers, also known as prime factors, in the process of prime factorization. The following actions are required for prime factorization.
1. We start by splitting the number in half using the lowest prime integer that does so precisely.
2. If the quotient is not exactly divided by the smallest prime number, we divide it again by the next smallest prime number. until the quotient equals 1, keep repeating the operation. Here, we only divide using prime numbers.
3. The result is the number itself, after multiplying all the prime factors.
In order to find the cube root using prime factorization, we must divide the factors into three groups, each of which must equal 5832.

5832 = (2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3) 5832 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 5832 = (2 \times 2 \times 2) \times (3 \times 3 \times 3) \times (3 \times 3 \times 3) 5832 = (2 \times 2 \times 2) \times (3 \times 3 \times 3) \times (3 \times 3 \times 3)

\sqrt[3]{5832}

=2×3×3. Therefore, we can write:

\sqrt[3]{5832} = 18

So, we got 5832 as the perfect cube of 18 .

Hence, the cube root of 5832 is 18

The cube root of 5832 is ____.

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