square root of x 2 y 2

Art Scpae

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15-10-2024

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Demystifying the Square Root of x²y²: A Step-by-Step Guide

The expression √(x²y²) might seem intimidating at first, but understanding the fundamentals of square roots and exponents can make it surprisingly simple. This article aims to guide you through the process of finding the square root of x²y², providing a clear and accessible explanation.

Understanding 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.

The Role of Exponents

In the expression x²y², the exponents "2" indicate that both x and y are multiplied by themselves:

• x² = x * x
• y² = y * y

Simplifying the Expression

Now, let's combine our understanding of square roots and exponents to simplify √(x²y²):

1. Separate the terms: We can rewrite the expression as √(x²) * √(y²) because the square root of a product is equal to the product of the square roots.
2. Apply the square root: The square root of x² is x, and the square root of y² is y.
3. Simplify: Therefore, √(x²y²) = √(x²) * √(y²) = x * y = xy

Important Note: While the solution xy is valid, it's crucial to remember that both x and y could be negative numbers. In such cases, the absolute value of xy, denoted as |xy|, would be the correct answer. This ensures that the square root is always a non-negative value.

Practical Example

Let's say x = -3 and y = 4. Applying our knowledge:

• x²y² = (-3)² * (4)² = 9 * 16 = 144
• √(x²y²) = √144 = 12

However, using the absolute value, |xy| = |-3 * 4| = |-12| = 12, which matches our previous calculation.

Conclusion

Finding the square root of x²y² boils down to understanding the properties of square roots and exponents. By applying these principles and remembering to consider the potential for negative values, you can confidently simplify this expression.

References:

• Understanding Square Roots - Math is Fun
• Exponents and Square Roots - Khan Academy

Keywords: square root, x²y², exponent, simplification, absolute value, algebra, mathematics, tutorial.