`sqrt(0.0000 4761)` equals

Options

A. 0.069
B. 0.0069
C. 0.00069
D. 0.0609

Answer

To find the square root of \(0.0004761\), we can follow these steps:

### Step 1: Rewrite the number in scientific notation
First, we can express \(0.0004761\) in scientific notation. This is done by moving the decimal point to the right until we have a number between 1 and 10.

\[ 0.0004761 = 4.761 \times 10^{-4} \]

### Step 2: Apply the square root to the scientific notation
Now, we can take the square root of both the coefficient and the power of ten:

\[ \sqrt{0.0004761} = \sqrt{4.761 \times 10^{-4}} = \sqrt{4.761} \times \sqrt{10^{-4}} \]

### Step 3: Simplify the square root of the power of ten
The square root of \(10^{-4}\) is:

\[ \sqrt{10^{-4}} = 10^{-2} \]

### Step 4: Calculate the square root of the coefficient
Next, we need to find \(\sqrt{4.761}\). This can be approximated or calculated using a calculator:

\[ \sqrt{4.761} \approx 2.18 \]

### Step 5: Combine the results
Now, we can combine the results from steps 3 and 4:

\[ \sqrt{0.0004761} = 2.18 \times 10^{-2} \]

### Step 6: Convert back to decimal notation
Finally, we convert \(2.18 \times 10^{-2}\) back to decimal notation:

\[ 2.18 \times 10^{-2} = 0.0218 \]

Thus, the square root of \(0.0004761\) is approximately \(0.0218\).

### Final Answer
\[ \sqrt{0.0004761} \approx 0.0218 \]