The integral part of 2+16 is

2+16+2-16=2 C0 6 26+C2 6 24+C4 6 22+C6 6 20 =2 8+60+30+1=1982+16=198-2-16Integal Part =[198-fraction] =197

The integral part of 2+16 is

2+16+2-16=2 C0 6 26+C2 6 24+C4 6 22+C6 6 20 =2 8+60+30+1=1982+16=198-2-16Integal Part =[198-fraction] =197

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The integral part of ${(\sqrt{2} + 1)}^{6}$ is

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198

199

197

196

answer is C.

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Detailed Solution

$\begin{array}{rcl} {(\sqrt{2} + 1)}^{6} + {(\sqrt{2} - 1)}^{6} & = & 2 [{}^{6}{C_{0}} {(\sqrt{2})}^{6} + {}^{6}{C_{2}} {(\sqrt{2})}^{4} + {}^{6}{C_{4}} {(\sqrt{2})}^{2} + {}^{6}{C_{6}} {(\sqrt{2})}^{0}] \\ = & 2 [8 + 60 + 30 + 1] = 198 \\ {(\sqrt{2} + 1)}^{6} & = & 198 - {(\sqrt{2} - 1)}^{6} \end{array}$