The Correct Answer and Explanation is:
Based on the structure of the question provided in the image, the correct answer is 2.
Explanation
The question asks for the common “radical part” of two mathematical expressions, which were presumably located in image files named mc002-1.Jpg and mc002-2.Jpg. Although these expressions are not visible, we can deduce the answer and the underlying mathematical concept from the question’s format.
The process required is to simplify radical expressions. Simplifying a radical means rewriting it so that the number under the radical sign, known as the radicand, has no perfect square factors (or perfect cube factors for a cube root, and so on). The “radical part” typically refers to the final radicand after this simplification. For example, to simplify the square root of 50 (√50), you would find the largest perfect square that divides 50, which is 25. You can then rewrite the expression:
√50 = √(25 × 2) = √25 × √2 = 5√2
In this simplified form, 5√2, the coefficient is 5, and the radicand, or the number remaining inside the radical, is 2.
The question implies that both expressions, once simplified, will share the same radicand. The text in the image concludes with a list of what appear to be multiple-choice options, also as image files, followed by the number “2”. This strongly suggests that “2” is the correct answer. This means that if we could see the original expressions, they would both simplify to a form where the radicand is 2. For instance, the expressions could have been √18 and √98.
Simplifying √18:
√18 = √(9 × 2) = 3√2
Simplifying √98:
√98 = √(49 × 2) = 7√2
In both of these examples, the final radicand is 2. Therefore, the radical part that is common to both simplified expressions is 2.
