Question

The 10th term of ${(3-\sqrt{\frac{17}{4}}+3\sqrt{2})}^{20}$ is

• A. an irrational number
• B. a rational number
• C. a positive integer
• D. a negative integer

Answer 1

The correct option is A an irrational number

Given, $\left(3\right(1-\sqrt{2})+\sqrt{\frac{17}{4}}{)}^{20}$
$T_{9+1}$
$={}^{20}{C}_9{3}^{11}(1-\sqrt{2}{)}^{11}(\sqrt{\frac{17}{4}}{)}^9$
$={}^{20}{C}_9{3}^{11}(1-\sqrt{2}{)}^{11}(\sqrt{\frac{17}{4}}{)}^9$
Hence the term will be irrational.