Binomial Theorem
Grade None
Question:
<p>The number of rational terms in the binomial expansion of <span class="math-tex">\((\sqrt{2}+\sqrt[3]{3})^{18}\)</span> is:</p>
<p style="display:inline">4</p>
<p style="display:inline">8</p>
<p style="display:inline">5</p>
<p style="display:inline">6</p>
Step-by-Step Solution
Key Concept: A term in the binomial expansion is rational only if the exponents of all prime bases in its general term are integers, which requires the index $r$ to be a multiple of the least common multiple of the radical denominators within the range $[0, n]$.
<p>4</p>
Correct Answer: A