Find cube root of `- 5832`.

Answer

To find the cube root of -5832, we will follow these steps:

### Step 1: Factor the Number
First, we need to factor the number 5832 into its prime factors.

1. Start dividing by the smallest prime number, which is 2.
- 5832 ÷ 2 = 2916
- 2916 ÷ 2 = 1458
- 1458 ÷ 2 = 729
- 729 is not divisible by 2, so we move to the next prime number, which is 3.
- 729 ÷ 3 = 243
- 243 ÷ 3 = 81
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So, the prime factorization of 5832 is:
\[ 5832 = 2^3 \times 3^6 \]

### Step 2: Incorporate the Negative Sign
Since we are looking for the cube root of -5832, we can express it as:
\[ -5832 = -1 \times 5832 = -1 \times (2^3 \times 3^6) \]

### Step 3: Find the Cube Root
Now we can find the cube root of each factor:
\[ \sqrt[3]{-5832} = \sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{3^6} \]

Calculating each part:
- The cube root of -1 is -1.
- The cube root of \(2^3\) is 2.
- The cube root of \(3^6\) is \(3^{6/3} = 3^2 = 9\).

### Step 4: Multiply the Results
Now, we multiply these results together:
\[ \sqrt[3]{-5832} = -1 \times 2 \times 9 = -18 \]

### Final Answer
Thus, the cube root of -5832 is:
\[ \sqrt[3]{-5832} = -18 \]

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