Question

If $P=\sqrt{16+8\sqrt{3}}-\sqrt{21-12\sqrt{3}}$, then the value of P is

• A. 8
• B. 6
• C. 5
• D. 4

Answer 1

The correct option is C 5

$P=\sqrt{16+8\sqrt{3}}-\sqrt{21-12\sqrt{3}}$
$\Rightarrow P=\sqrt{{\left(2\right)}^2+{\left(2\sqrt{3}\right)}^2+2\times 2\times 2\sqrt{3}}-\sqrt{{\left(3\right)}^2+{\left(2\sqrt{3}\right)}^2-2\times 3\times 2\sqrt{3}}$
$\Rightarrow P=\sqrt{{(2+2\sqrt{3})}^2}-\sqrt{{(2\sqrt{3}-3)}^2}$
$\Rightarrow P=(2+2\sqrt{3})-(2\sqrt{3}-3)$
$\Rightarrow P=2+2\sqrt{3}-2\sqrt{3}+3$
$\Rightarrow P=5$
Hence, the correct answer is option c.