Question

The number of rational terms in ${(1+\sqrt{2}+\sqrt[8]{83})}^{6}is$

• A. 6
• B. 7
• C. 5
• D. 8

Answer 1

The correct option is B

7

${(1+\sqrt{2}+\sqrt[8]{83})}^6{=}^6{C}_0{+}^6{C}_1(\sqrt{2}+\sqrt[8]{83}){+}^6{C}_2{(\sqrt{2}+\sqrt[8]{83})}^3+\cdots {+}^6{C}_6{(\sqrt{2}+\sqrt[8]{83})}^6$

$In{(\sqrt{2}+\sqrt[8]{83})}^6,T_{r+1}{=}^6{C}_r(\sqrt{2}{)}^{6-r}.{\left(\sqrt[8]{83}\right)}^r$

It is rational if r = 0, 6. Similarly in other cases

$\therefore$ The number of rational terms = 1 + 0 + 1 + 1 + 1 + 1 + 2 = 7