`sqrt(0.00059049)=?`

Options

A. 0.243
B. 0.0243
C. 0.00243
D. 0.000243

Answer

To solve the problem \( \sqrt{0.00059049} \), we will follow a systematic approach to find the square root step by step.

### Step 1: Rewrite the number in a more manageable form
We can express \( 0.00059049 \) in scientific notation:
\[ 0.00059049 = 5.9049 \times 10^{-4} \]

### Step 2: Find the square root of the coefficient
Now, we need to find the square root of \( 5.9049 \):
\[ \sqrt{5.9049} \]

### Step 3: Estimate the square root
To estimate \( \sqrt{5.9049} \), we can look for perfect squares close to \( 5.9049 \). We know that:
\[ 2.4^2 = 5.76 \quad \text{and} \quad 2.5^2 = 6.25 \]
Thus, \( \sqrt{5.9049} \) is approximately \( 2.4 \).

### Step 4: Calculate the exact square root
Using a calculator or more precise methods, we find:
\[ \sqrt{5.9049} = 2.43 \]

### Step 5: Combine the results
Now we need to consider the exponent from the scientific notation:
\[ \sqrt{0.00059049} = \sqrt{5.9049 \times 10^{-4}} = \sqrt{5.9049} \times \sqrt{10^{-4}} = 2.43 \times 10^{-2} \]

### Step 6: Final result
Thus, we have:
\[ \sqrt{0.00059049} = 0.0243 \]

### Conclusion
The final answer is:
\[ \sqrt{0.00059049} = 0.0243 \]