**Question:**

In the expansion \({\left( {x + \frac{2}{{\sqrt x }}} \right)^6}\), the coefficient of \({x^3},\left( {x) > 0} \right)\) is:

**Reference explanation:**

**Correct answer:**

The general term in the above expansion is

\({T_{k + 1}} = C_6^k. {x^{6 – k}}{2^k}. {x^{ – \frac{1}{2}k}}\)

Requires the problem to occur when

\(6 – k – \frac{1}{2}k = 3 \Leftrightarrow k = 3\)

Then the coefficient of x^{3 }is: \(C_6^3{.2^3} = 160\).

ADSENSE

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