`sqrt(5)+sqrt(2)` is

Options

A. rational number
B. prime number
C. irrational number
D. composite number

Answer

To determine the nature of the expression \(\sqrt{5} + \sqrt{2}\), we can follow these steps:

### Step 1: Identify the numbers
First, we recognize that both \(\sqrt{5}\) and \(\sqrt{2}\) are square roots of non-perfect squares.

### Step 2: Determine if they are rational or irrational
- \(\sqrt{5}\) is an irrational number because it cannot be expressed as a fraction of two integers.
- \(\sqrt{2}\) is also an irrational number for the same reason.

### Step 3: Add the two irrational numbers
Now, we need to add these two irrational numbers:
\[ \sqrt{5} + \sqrt{2} \]

### Step 4: Analyze the sum of two irrational numbers
The sum of two irrational numbers can be either rational or irrational. However, in this case, we need to check if \(\sqrt{5} + \sqrt{2}\) can be expressed as a rational number.

### Step 5: Conclusion
Since \(\sqrt{5}\) and \(\sqrt{2}\) do not have a common rational representation, their sum \(\sqrt{5} + \sqrt{2}\) remains irrational.

Thus, we conclude that:
\[ \sqrt{5} + \sqrt{2} \text{ is an irrational number.} \]

---