Find cube root of `-17576`.

Answer

To find the cube root of \(-17576\), we can follow these steps:

### Step 1: Identify the number
We need to find the cube root of \(-17576\).

### Step 2: Understand cube roots
The cube root of a number \(x\) is a number \(y\) such that \(y^3 = x\). In this case, we are looking for a number \(y\) such that \(y^3 = -17576\).

### Step 3: Find the cube root
Since the number is negative, we can first find the cube root of the positive version of the number, \(17576\), and then apply the negative sign.

### Step 4: Calculate the cube root of \(17576\)
We can start by estimating the cube root. We can check the cubes of integers:

- \(20^3 = 8000\)
- \(30^3 = 27000\)

Since \(17576\) is between \(20^3\) and \(30^3\), we can try numbers between \(20\) and \(30\).

- \(25^3 = 15625\)
- \(26^3 = 17576\)

Thus, we find that \(26^3 = 17576\).

### Step 5: Apply the negative sign
Since we are looking for the cube root of \(-17576\), we take the negative of \(26\).

### Final Answer
The cube root of \(-17576\) is \(-26\).

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