Find the number of terms in the
expansion of `(root(2)(9) + root(2)(8) )^(500) ` which are integers .

Explanation

To find the number of integer terms in the expansion of \((\sqrt{9} + \sqrt{8})^{500}\), we will follow these steps:

### Step 1: Rewrite the Terms
First, we rewrite the terms \(\sqrt{9}\) and \(\sqrt{8}\):
\[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{8} = 2\sqrt{2} \]
Thus, we can express the original expression as:
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