Question

The integer next above $(\sqrt{3}+1{)}^{2n}$ contains

• A. $2^{n+1}$ as a factor
• B. $2^{n+2}$ as a factor
• C. $2^{n+3}$ as a factor
• D. $2^n$ as a factor

Answer 1

The correct option is D $2^n$ as a factor

We have,

$(\sqrt{3}+1{)}^{2n}$

$=$ $\left\{\right(\sqrt{3}+1{)}^2{\}}^n$

$=(4+2\sqrt{3}{)}^n$

$=2^n(2+\sqrt{3}{)}^n$.

So it is clear that the integer next above the given number contains $2^n$ as a factor.