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Square roots are a fundamental aspect of algebra that help us find a number which, when multiplied by itself, results in the given number. For example, the square root of 36 is 6, because 6 times 6 is 36. Mathematically, this is shown as \( \sqrt{36} = 6 \). When dealing with variables, the square root works similarly. If you have a term like \( x^2 \), you can find its square root by dividing the power by 2, resulting in \( x \). This is why finding the square roots of algebraic expressions involves simplifying both numbers and variables separately. By understanding how square roots function, you can simplify complex mathematical problems more effectively.

Multiplying radicals involves a few straightforward rules. Radicals are numbers or expressions under a square root sign. When you're multiplying them, you should do so in steps.

• First, multiply the numbers inside the square root signs together.
• Then, simplify the resulting square root, if possible.

For instance, considering the expression \( \sqrt{18} \times \sqrt{2} \), the multiplication inside the radical gives us \( \sqrt{18 \times 2} = \sqrt{36} \).This equals 6 because 6 multiplied by itself yields 36. This approach allows for more orderly and understandable calculations, whether it involves integers or algebraic expressions.

Simplification is the process of reducing an expression to its simplest form. This involves breaking down each part of the expression and combining them as efficiently as possible. In the given problem:1. We first computed the square root of the coefficients, which were 18 and 2. The product is 36, and its square root is 6. 2. Next, we calculated the square root of the variables. Since \( x^2 \) becomes \( x \), and \( y \) remains under the square root as \( \sqrt{y} \), it was simplified to \( 6x\sqrt{y} \). 3. The final step was to multiply these simplified parts: \( 6x\sqrt{y} \times x\sqrt{y} = 6x^2y \).By following the step-by-step approach to simplify each component, you reach an expression that's much easier to work with or interpret.