Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy

Verified step by step guidance

1. Identify the like terms in the expression. Both terms involve the square root of the product \(xy\), so they can be combined.
2. Rewrite the expression to clearly show the square root terms: \$3\sqrt{xy} - 8\sqrt{xy}$.
3. Since both terms have the same radical part \(\sqrt{xy}\), factor it out: \((3 - 8)\sqrt{xy}\).
4. Perform the subtraction inside the parentheses: \$3 - 8 = -5$.
5. Write the simplified expression as \(-5\sqrt{xy}\).

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots, applied to variables or numbers. Understanding how to interpret and manipulate these expressions is essential for simplifying or performing operations on them.

Like Radicals

Like radicals have the same index and radicand (the expression inside the root). Only like radicals can be combined through addition or subtraction, similar to combining like terms in algebra.

Simplifying Radicals

Simplifying radicals involves rewriting the expression to its simplest form by factoring out perfect powers or combining terms. This process helps in reducing expressions and making operations like addition or subtraction possible.