Question

Find the square root of $7-4\sqrt{3}$

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

Answer 1

The correct option is C $2-\sqrt{3}$

$7-4\sqrt{3}$

$=7-2\sqrt{2\times 3}$

$=7-2\sqrt{12}$

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

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

$\therefore \sqrt{7-}4\sqrt{3}=2-\sqrt{3}$

$2-\sqrt{3}$