If  x  =  5√5 + √4  and  y  =  6√5 − √4  then  x + y  isSelect an answerA 11√5 − √4 B 11√5 + 2 C √5 + √4 D √5 + 11√4

1. Break Down the Problem

We are given two variables:

• $x = 5\sqrt{5} + \sqrt{4}$
• $y = 6\sqrt{5} - \sqrt{4}$

We need to find $x + y$.

2. Relevant Concepts

To find $x + y$, we will combine the two expressions algebraically.

3. Analysis and Detail

Let's calculate $x + y$:

$x + y = (5\sqrt{5} + \sqrt{4}) + (6\sqrt{5} - \sqrt{4})$

Combine like terms:

• For the $\sqrt{5}$ terms: $5\sqrt{5} + 6\sqrt{5} = 11\sqrt{5}$
• For the constant terms: $\sqrt{4} - \sqrt{4} = 0$

Thus, we have: $x + y = 11\sqrt{5}$

4. Verify and Summarize

We combined both variables and simplified to find that the $\sqrt{4}$ terms cancel each other out completely.

Final Answer

The result is: $x + y = 11\sqrt{5}$

Since this matches with none of the provided options, let's find the nearest match in terms of format. The calculation confirms that neither of the available choices is $11\sqrt{5}$, hence it appears there may be an error in options or original calculation context. However, based on our calculations, the correct answer is $11\sqrt{5}$.