Question

The value of the expansion $(\sqrt{3}+1{)}^5+(\sqrt{3}-1{)}^5$

• A. $88$
• B. $40$
• C. $88$$\sqrt{3}$
• D. $40$$\sqrt{3}$

Answer 1

Answer: (C)

$88$$\sqrt{3}$

In the expansion of the above expression, all the even terms will be eliminated, and we would be left with
$2\left[\right(\sqrt{3}{)}^5+10\left(\right(\sqrt{3}{)}^3+5\left(\sqrt{3}{)}^1\right]$
$=2[9\sqrt{3}+30\sqrt{3}+5\sqrt{3}]$

$=2\times 44\sqrt{3}$

$=88\sqrt{3}$