%5E1%2F2.jpeg "(-49)^1/2")
Understanding (-49)^1/2
The expression (-49)^1/2 represents the square root of -49. Here's a breakdown of what this means and why it's important to understand:
The Concept of Square Roots
A square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3 because 3 * 3 = 9.
Dealing with Negative Numbers
The issue with (-49)^1/2 is that there is no real number that, when multiplied by itself, results in -49. This is because squaring any real number (positive or negative) always produces a positive result.
Introducing Complex Numbers
To address this, we introduce the concept of complex numbers. Complex numbers are an extension of real numbers that include the imaginary unit i, defined as the square root of -1.
Therefore, (-49)^1/2 is equal to 7i. This is because 7i * 7i = -49.
Key Takeaways
- The square root of a negative number is not a real number.
- Complex numbers are necessary to represent the square roots of negative numbers.
- (-49)^1/2 is a complex number represented as 7i.