$$ \sqrt{\frac{1643684-\frac{\left(4282\right)^2}{10}}{9}} $$

It seems there's a problem with the calculation, specifically a math domain error. This usually happens when attempting to take the square root of a negative number. Let's break down the expression step by step to identify the issue.

The expression is:

\[
\sqrt{\frac{1643684 - \frac{4282^2}{10}}{9}}
\]

First, I'll calculate $ \frac{4282^2}{10} $ and then subtract it from 1643684. After that, I'll check if the resulting value is negative or positive.The result of $ 1643684 - \frac{4282^2}{10} $ is approximately $-189868.4$, which is negative. Since the square root of a negative number is not defined in the set of real numbers, this is why we encountered the error.

Would you like to proceed with finding the complex (imaginary) solution, or do you want to explore a different approach?

This problem involves calculating the square root of a complex arithmetic expression, $$ \sqrt{\frac{1643684-\frac{\left(4282\right)^2}{10}}{9}} $$, which leads to a math domain error due to the square root of a negative number. Learn how to break down the steps and explore potential solutions, including imaginary numbers. Suitable for Grades 10-12.

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