Find the cube root of 125.

Answer

To find the cube root of 125, we can follow these steps:

### Step 1: Factor the number 125
We start by breaking down 125 into its prime factors.

- Divide 125 by 5 (the smallest prime number):
\[ 125 \div 5 = 25 \]

- Now, divide 25 by 5:
\[ 25 \div 5 = 5 \]

- Finally, divide 5 by 5:
\[ 5 \div 5 = 1 \]

So, the prime factorization of 125 is:
\[ 125 = 5 \times 5 \times 5 = 5^3 \]

### Step 2: Understand the concept of cube root
The cube root of a number \( x \) is a number \( y \) such that:
\[ y^3 = x \]
In our case, we want to find \( y \) such that:
\[ y^3 = 125 \]

### Step 3: Apply the cube root to the factorization
Since we have found that:
\[ 125 = 5^3 \]
We can now find the cube root:
\[ \sqrt[3]{125} = \sqrt[3]{5^3} \]

### Step 4: Simplify the cube root
Using the property of cube roots, we can simplify:
\[ \sqrt[3]{5^3} = 5 \]

### Conclusion
Thus, the cube root of 125 is:
\[ \boxed{5} \]

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