If the square root of 841 is 29, then the square root of 0.00000841 is equal to :

Options

A. 0.029
B. 0.0029
C. 0.00029
D. 0.29

Answer

To find the square root of 0.00000841 given that the square root of 841 is 29, we can follow these steps:

### Step 1: Understand the relationship between the numbers
We know that:
\[ \sqrt{841} = 29 \]
This means that 841 can be expressed as \(29^2\).

### Step 2: Rewrite the number 0.00000841
We can express 0.00000841 in scientific notation:
\[ 0.00000841 = 8.41 \times 10^{-6} \]

### Step 3: Separate the components
We can separate the square root of the product:
\[ \sqrt{0.00000841} = \sqrt{8.41 \times 10^{-6}} = \sqrt{8.41} \times \sqrt{10^{-6}} \]

### Step 4: Calculate the square root of \(10^{-6}\)
The square root of \(10^{-6}\) is:
\[ \sqrt{10^{-6}} = 10^{-3} = 0.001 \]

### Step 5: Calculate the square root of 8.41
Now, we need to find \(\sqrt{8.41}\). Since \(8.41 = \frac{841}{100}\), we can use the square root we already know:
\[ \sqrt{8.41} = \sqrt{\frac{841}{100}} = \frac{\sqrt{841}}{\sqrt{100}} = \frac{29}{10} = 2.9 \]

### Step 6: Combine the results
Now, we can combine our results:
\[ \sqrt{0.00000841} = \sqrt{8.41} \times \sqrt{10^{-6}} = 2.9 \times 0.001 = 0.0029 \]

### Final Answer
Thus, the square root of 0.00000841 is:
\[ \boxed{0.0029} \]

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