`root(3)(0.000125)` is equal to

Options

A. 0.5
B. 0.15
C. 0.05
D. 0.005

Answer

To solve the problem \( \sqrt[3]{0.000125} \), we will follow these steps:

### Step 1: Rewrite the number in a fraction form
We can express \( 0.000125 \) as a fraction:
\[ 0.000125 = \frac{125}{1000000} \]

### Step 2: Simplify the fraction
Next, we can simplify the fraction:
\[ \frac{125}{1000000} = \frac{125}{10^6} \]

### Step 3: Factor the numerator and denominator
Now, we can factor \( 125 \) and \( 10^6 \):
\[ 125 = 5^3 \quad \text{and} \quad 10^6 = (10^2)^3 = 100^3 = (10^2 \cdot 10^2 \cdot 10^2) = (100)^3 \]

### Step 4: Rewrite in terms of cube roots
Now we can rewrite the expression using cube roots:
\[ \sqrt[3]{0.000125} = \sqrt[3]{\frac{5^3}{10^6}} = \frac{\sqrt[3]{5^3}}{\sqrt[3]{10^6}} \]

### Step 5: Calculate the cube roots
Calculating the cube roots gives us:
\[ \sqrt[3]{5^3} = 5 \quad \text{and} \quad \sqrt[3]{10^6} = 10^2 = 100 \]

### Step 6: Combine the results
Now we can combine the results:
\[ \sqrt[3]{0.000125} = \frac{5}{100} = 0.05 \]

### Final Answer
Thus, the value of \( \sqrt[3]{0.000125} \) is:
\[ \boxed{0.05} \]

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