What is the simplified value of `sqrt(((0.07)^2 + (0.29)^2 - 0.0203)/((0.07)^3 + (0.29)^3)) ?`

Options

A. 0.6
B. 0.06
C. `(1//0.6)`
D. `(1//0.06)`

Answer

To solve the expression \( \sqrt{\frac{(0.07)^2 + (0.29)^2 - 0.0203}{(0.07)^3 + (0.29)^3}} \), we will follow these steps:

### Step 1: Calculate \( (0.07)^2 \) and \( (0.29)^2 \)
\[ (0.07)^2 = 0.0049 \]
\[ (0.29)^2 = 0.0841 \]

### Step 2: Add \( (0.07)^2 \) and \( (0.29)^2 \)
\[ 0.0049 + 0.0841 = 0.089 \]

### Step 3: Subtract \( 0.0203 \) from the result of Step 2
\[ 0.089 - 0.0203 = 0.0687 \]

### Step 4: Calculate \( (0.07)^3 \) and \( (0.29)^3 \)
\[ (0.07)^3 = 0.000343 \]
\[ (0.29)^3 = 0.024389 \]

### Step 5: Add \( (0.07)^3 \) and \( (0.29)^3 \)
\[ 0.000343 + 0.024389 = 0.024732 \]

### Step 6: Substitute the results into the expression
Now we have:
\[ \sqrt{\frac{0.0687}{0.024732}} \]

### Step 7: Calculate the division
\[ \frac{0.0687}{0.024732} \approx 2.776 \]

### Step 8: Take the square root of the result
\[ \sqrt{2.776} \approx 1.67 \]

### Final Answer
The simplified value is approximately \( 1.67 \).

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