The Correct Answer and Explanation is:
The correct answer is 2.
The image provides a question that asks for the common radical part of two different expressions after they are simplified. The expressions themselves are not shown but are referred to by the filenames mc002-1. Jpg and mc002-2. Jpg. The image also lists potential answer choices, which include other filenames and the number 2. Although the specific expressions are missing, the question can be answered by understanding the mathematical concepts involved and making a logical inference based on the provided answer choice.
In mathematics, a radical expression consists of a radical symbol (like the square root symbol, √), a number or expression inside the symbol called the radicand, and a coefficient outside. The “radical part” refers to this radicand. To simplify a radical expression, we factor the radicand to find the largest possible perfect square (or cube, etc., depending on the root). This perfect square factor is then taken out of the radical. For example, to simplify √20, we recognize that 20 = 4 × 5. Since 4 is a perfect square, we can rewrite this as √4 × √5, which simplifies to 2√5. In this simplified form, the coefficient is 2 and the radical part (radicand) is 5.
The question asks for the radical part that is the same for two different expressions. Let’s consider a hypothetical example. Suppose the two expressions were √8 and √50.
- Simplify √8: The largest perfect square that divides 8 is 4. So, √8 = √(4 × 2) = √4 × √2 = 2√2. The radical part is 2.
- Simplify √50: The largest perfect square that divides 50 is 25. So, √50 = √(25 × 2) = √25 × √2 = 5√2. The radical part is 2.
In this case, both expressions, once simplified, have a common radical part of 2. Since 2 is provided as a potential answer in the problem, it is highly probable that the unseen expressions in mc002-1. Jpg and mc002-2. Jpg are similar radicals that both reduce to a form with a radicand of 2.
