Question

Let [x] denote the greatest integer less than or equal to x. If $x=(\sqrt{3}+1{)}^5$ then [x] is equal to

• A. 75
• B. 50
• C. 76
• D. 152.

Answer 1

Answer: (D)

$x={\left(\sqrt{3}+1\right)}^5=I+f$
where $0\le f<1$ and $I\in Z$
$f={\left(\sqrt{3}+1\right)}^5;0\le f<1$
$I+f-f=2\left[5{\left(\sqrt{3}\right)}^4+10{\left(\sqrt{3}\right)}^2+1\right]$
which is an integer.
$\therefore I=152$