Final answer:
Mathematical operations on the radical pairs involve adding, subtracting, multiplying, and dividing, but can only be done directly if the radicals have the same index and radicand. Operations should be followed by simplification to ensure the answer is in its simplest form.
Step-by-step explanation:
The student's question involves performing arithmetic operations on pairs of radicals: finding the sum, the difference, the product, and the quotient. It is important to initially clarify that the provided information is not directly related to the arithmetic of radicals but rather to chemical equations and stoichiometry. However, I will directly address the student's question about operations with radicals.
Operations with Radicals
Sum of Radicals: To find the sum, simply add the two radicals together if they have the same radicand. If not, they cannot be directly added.
Subtraction of Radicals: Similarly, subtract one radical from the other if they share the same radicand; otherwise, they remain separate terms.
Product of Radicals: Multiplication involves taking the product of the two radicands, provided both radicals are of the same index.
Division of Radicals: When dividing, simplify the radical expression by dividing the radicands while ensuring both have the same index, and then simplify further if possible.
Remember to check your final answer to ensure all expressions are simplified and reasonable.