Find the sum $6 y \sqrt{a}+7 y \sqrt{a}$.
Answer (1)
Identify like terms: 6 y a and 7 y a .
Combine like terms by adding their coefficients: ( 6 + 7 ) y a .
Simplify the expression: 13 y a .
The final answer is 13 y a .
Explanation
Understanding the Problem We are asked to find the sum of two terms: 6 y a and 7 y a . Both terms contain the same variables y and a .
Combining Like Terms To find the sum of the two terms, we can combine them by adding their coefficients. This is similar to combining like terms in algebra.
Factoring Common Term We have 6 y a + 7 y a . We can factor out the common term y a from both terms: ( 6 + 7 ) y a
Performing Addition Now, we perform the addition inside the parentheses: 6 + 7 = 13 So, the expression becomes: 13 y a
Final Answer Therefore, the sum of 6 y a and 7 y a is 13 y a .
Examples
In physics, if you're calculating the total momentum of two objects with similar properties, you might encounter an expression like 6 y a + 7 y a , where y represents velocity and a represents mass. Simplifying this expression to 13 y a helps in quickly determining the combined momentum without needing to perform separate calculations for each object. This kind of simplification is crucial in fields like engineering and physics for efficient problem-solving.
