If the cube root of 132651 is 51, then what is the value of
`root3(132.651)+root(3)0.132651+root3(0.000132651)`

Answer

To solve the expression \( \sqrt[3]{132.651} + \sqrt[3]{0.132651} + \sqrt[3]{0.000132651} \), we can use the fact that the cube root of 132651 is given as 51. Let's break it down step by step.

### Step 1: Rewrite the expression using the known cube root
We know that:
\[ \sqrt[3]{132651} = 51 \]
Now, we can express the other terms in the expression in terms of 132651.

### Step 2: Analyze each term
1. **First term**:
\[ \sqrt[3]{132.651} = \sqrt[3]{\frac{132651}{1000}} = \frac{\sqrt[3]{132651}}{\sqrt[3]{1000}} = \frac{51}{10} = 5.1 \]

2. **Second term**:
\[ \sqrt[3]{0.132651} = \sqrt[3]{\frac{132651}{1000000}} = \frac{\sqrt[3]{132651}}{\sqrt[3]{1000000}} = \frac{51}{100} = 0.51 \]

3. **Third term**:
\[ \sqrt[3]{0.000132651} = \sqrt[3]{\frac{132651}{1000000000}} = \frac{\sqrt[3]{132651}}{\sqrt[3]{1000000000}} = \frac{51}{1000} = 0.051 \]

### Step 3: Combine the results
Now we can add the results from each term:
\[ 5.1 + 0.51 + 0.051 \]

### Step 4: Perform the addition
1. First, add \( 5.1 + 0.51 \):
\[ 5.1 + 0.51 = 5.61 \]

2. Now add \( 5.61 + 0.051 \):
\[ 5.61 + 0.051 = 5.661 \]

### Final Answer
Thus, the value of the expression \( \sqrt[3]{132.651} + \sqrt[3]{0.132651} + \sqrt[3]{0.000132651} \) is:
\[ \boxed{5.661} \]