The expression you provided, \(\sqrt{-49} \times x\), contains the square root of a negative number. In mathematics, the square root of a negative number involves complex numbers.

\[
\sqrt{-49} = \sqrt{49} \times \sqrt{-1} = 7i
\]

Here, \(i\) is the imaginary unit, which satisfies \(i^2 = -1\). So, the expression becomes:

\[
\sqrt{-49} \times x = 7i \times x = 7ix
\]

Thus, the simplified form of the expression is \(7ix\), where \(i\) represents the imaginary unit.

Would you like more details on imaginary numbers or complex expressions?

Here are some related questions for further practice:
1. What is \(\sqrt{-36} \times 3x\)?
2. How would you simplify \((5i)^2\)?
3. What is the product of \((3 + 2i) \times (1 - i)\)?
4. What is the magnitude of the complex number \(7i\)?
5. How do you solve the quadratic equation \(x^2 + 49 = 0\)?

**Tip:** When dealing with square roots of negative numbers, remember that they always involve imaginary numbers using \(i = \sqrt{-1}\).

Explore how to simplify the expression √(-49)x using complex numbers. This problem highlights key algebraic concepts and introduces the imaginary unit i, perfect for students in Grades 9-12.

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