91Ó°ÊÓ

When multiplying radicals, start by focusing on the numbers inside the radical signs. Radicals usually denote square roots, but the process is consistent even with different roots, as long as they are like radicals. In our exercise, the radicals were identical, being \( \sqrt{1} \), which simplified down very easily.
To multiply radicals, first multiply the numbers outside the radical signs (these numbers are called coefficients). Then multiply the contents inside the radicals. Ideally, this multiplication should follow the order:

• Multiply the coefficients together.
• Multiply the numbers inside the radicals.

After multiplication, if any simplification can be done, it will make the expression easier to understand and calculate. Here, because \( \sqrt{1} \) is simply 1, the radical part becomes irrelevant beyond initial simplification.

Simplifying radicals often reduces the complexity of a mathematical expression. A key step in this process involves understanding what the radical symbol \( \sqrt{} \) represents. In the given problem, since we work with \( \sqrt{1} \), the value remains 1, because the square root of 1 is 1.
When simplifying, aim to reduce the numbers within the radical as much as possible. Sometimes, the number under the square root sign is not a perfect square, but it can be broken down into factors, some of which are perfect squares. For instance, \( \sqrt{4} \) can be simplified to 2 because 4 is a perfect square.
Always check whether the number under your radical can be simplified to make the expression easier to handle. But keep in mind, all variables and numbers should remain non-negative to retain consistency.

Multiplying coefficients is straightforward arithmetic, involving only the whole numbers in front of the radicals. In our given problem, the coefficients were 2 and 6. These were multiplied directly as regular numbers:

• 2 multiplied by 6 equals 12.

This gives us 12, the coefficient that multiplies the simplified radical (in this case, 1).
When working through these calculations, it is important to understand that coefficients still maintain their separate integrity from the radicals themselves, unless simplified altogether. Coefficients represent a scaling factor for the radical expression and combining them properly is essential for the final result.
The process remains simple: treat the coefficients as standalone numbers while multiplying, and ensure any multiplication outcome is reflected in the overall expression.