Find the square root of `((0.064-0.008)(0.16-0.04))/((0.16+0.08+0.04)(0.4+0.2)^(3))`

Options

A. `2/3`
B. `1/3`
C. 3
D. `3/2`

Answer

To find the square root of the expression \(\frac{(0.064 - 0.008)(0.16 - 0.04)}{(0.16 + 0.08 + 0.04)(0.4 + 0.2)^3}\), we can follow these steps:

### Step 1: Simplify the Numerator
First, we simplify the terms in the numerator:

1. Calculate \(0.064 - 0.008\):
\[ 0.064 - 0.008 = 0.056 \]

2. Calculate \(0.16 - 0.04\):
\[ 0.16 - 0.04 = 0.12 \]

3. Now, multiply these results:
\[ 0.056 \times 0.12 \]

### Step 2: Calculate the Product
Now we calculate the product:
\[ 0.056 \times 0.12 = 0.00672 \]

### Step 3: Simplify the Denominator
Next, we simplify the denominator:

1. Calculate \(0.16 + 0.08 + 0.04\):
\[ 0.16 + 0.08 + 0.04 = 0.28 \]

2. Calculate \(0.4 + 0.2\):
\[ 0.4 + 0.2 = 0.6 \]

3. Now calculate \((0.6)^3\):
\[ (0.6)^3 = 0.216 \]

4. Now multiply the results:
\[ 0.28 \times 0.216 \]

### Step 4: Calculate the Product
Now we calculate the product:
\[ 0.28 \times 0.216 = 0.06048 \]

### Step 5: Form the Fraction
Now we can form the fraction:
\[ \frac{0.00672}{0.06048} \]

### Step 6: Simplify the Fraction
Now simplify the fraction:
\[ \frac{0.00672}{0.06048} = \frac{672}{6048} = \frac{1}{9} \]

### Step 7: Find the Square Root
Now, we need to find the square root of \(\frac{1}{9}\):
\[ \sqrt{\frac{1}{9}} = \frac{1}{3} \]

### Final Answer
Thus, the square root of the given expression is:
\[ \frac{1}{3} \]