Question

If $a^3=11\sqrt{2}+9\sqrt{3},$ then $a$ is

• A. $\sqrt{3}+\sqrt{2}$
• B. $\sqrt{2}+\sqrt{6}$
• C. $\sqrt{3}+\sqrt{6}$
• D. $\sqrt{3}+\sqrt{5}$

Answer 1

The correct option is A $\sqrt{3}+\sqrt{2}$

$a^3=11\sqrt{2}+9\sqrt{3}$
$\Rightarrow a^3=2\sqrt{2}+9\sqrt{2}+3\sqrt{3}+6\sqrt{3}$
$\Rightarrow a^3=(\sqrt{2}{)}^3+(\sqrt{3}{)}^3+3\sqrt{6}(\sqrt{2}+\sqrt{3})$
$\Rightarrow a^3=(\sqrt{2}+\sqrt{3}{)}^3$
$\Rightarrow a=\sqrt{2}+\sqrt{3}$