If the cube root of 79507 is 43, then the value of `root(3)(79.507) + root(3)(0.079507) + root(3)(0.000079507)` is

Options

A. 0.4773
B. 477.3
C. 47.73
D. 4.773

Answer

To solve the problem, we need to find the value of the expression:

\[ \sqrt[3]{79.507} + \sqrt[3]{0.079507} + \sqrt[3]{0.000079507} \]

Given that the cube root of 79507 is 43, we can express the numbers in the cube roots in terms of 79507.

### Step 1: Rewrite the terms in the expression

We know that:

- \( 79.507 = \frac{79507}{1000} \)
- \( 0.079507 = \frac{79507}{1000000} \)
- \( 0.000079507 = \frac{79507}{1000000000} \)

### Step 2: Apply the cube root property

Using the property of cube roots, we can rewrite each term:

\[ \sqrt[3]{79.507} = \sqrt[3]{\frac{79507}{1000}} = \frac{\sqrt[3]{79507}}{\sqrt[3]{1000}} = \frac{43}{10} = 4.3 \]

\[ \sqrt[3]{0.079507} = \sqrt[3]{\frac{79507}{1000000}} = \frac{\sqrt[3]{79507}}{\sqrt[3]{1000000}} = \frac{43}{100} = 0.43 \]

\[ \sqrt[3]{0.000079507} = \sqrt[3]{\frac{79507}{1000000000}} = \frac{\sqrt[3]{79507}}{\sqrt[3]{1000000000}} = \frac{43}{1000} = 0.043 \]

### Step 3: Add the results

Now we can add these three results together:

\[ 4.3 + 0.43 + 0.043 \]

To make the addition easier, we can align the decimal points:

\[ \begin{array}{r} 4.300 \\ + 0.430 \\ + 0.043 \\ \hline 4.773 \\ \end{array} \]

### Final Result

Thus, the value of the expression is:

\[ \sqrt[3]{79.507} + \sqrt[3]{0.079507} + \sqrt[3]{0.000079507} = 4.773 \]