The value of `sqrt(((0.03)^(2) + (0.21)^(2) + (0.065)^(2))/((0.003)^(2) + (0.021)^(2) + (0.0065)^(2)))`

Options

A. 0.1
B. 10
C. `10^(2)`
D. `10^(3)`

Answer

To solve the expression

\[ \sqrt{\frac{(0.03)^2 + (0.21)^2 + (0.065)^2}{(0.003)^2 + (0.021)^2 + (0.0065)^2}} \]

we will follow these steps:

### Step 1: Calculate the squares of the numbers in the numerator and denominator.

**Numerator:**
- \((0.03)^2 = 0.0009\)
- \((0.21)^2 = 0.0441\)
- \((0.065)^2 = 0.004225\)

Now, add these values together:
\[ 0.0009 + 0.0441 + 0.004225 = 0.049225 \]

**Denominator:**
- \((0.003)^2 = 0.000009\)
- \((0.021)^2 = 0.000441\)
- \((0.0065)^2 = 0.00004225\)

Now, add these values together:
\[ 0.000009 + 0.000441 + 0.00004225 = 0.00049225 \]

### Step 2: Substitute the results back into the expression.

Now we have:
\[ \sqrt{\frac{0.049225}{0.00049225}} \]

### Step 3: Simplify the fraction inside the square root.

To simplify:
\[ \frac{0.049225}{0.00049225} = 100 \]

### Step 4: Take the square root.

Now we take the square root:
\[ \sqrt{100} = 10 \]

### Final Answer:
The value of the expression is \(10\).

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