To find the real-number root of [tex]\( \sqrt{941} \)[/tex] and round the answer to the nearest thousandth, follow these steps:
1. Calculate the square root: First, you need to find the square root of 941. Using a calculator, you find that the square root of 941 is approximately 30.675723300355934.
2. Round to the nearest thousandth: Next, you need to round this value to the nearest thousandth. The thousandth place is the third digit to the right of the decimal point. Thus, you examine the fourth digit to determine whether to round up or stay the same:
- The number is 30.675723300355934.
- The third decimal place is 5, and the fourth decimal place is 7.
3. Determine rounding: Since the fourth decimal place (7) is greater than or equal to 5, you round the third decimal place up by one.
So, rounding 30.675723300355934 to the nearest thousandth gives you:
[tex]\[
\sqrt{941} \approx 30.676
\][/tex]
Thus, the square root of 941, rounded to the nearest thousandth, is [tex]\(\boxed{30.676}\)[/tex].
