Question

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

• A. $2-\sqrt{3}$
• B. $5-\sqrt{3}$
• C. $2-\sqrt{5}$
• D. none of these

Answer 1

Answer: (A)

$2-\sqrt{3}$

Here $A=7,\sqrt{B}=4\sqrt{3}$
$\therefore A^2-B=C^2\Rightarrow 49-48=1andC=1$
$\therefore A+C=7+1=8,A-C=7-1=6$
$\therefore x=4,y=3$
$\therefore \sqrt{x}-\sqrt{y}=\sqrt{A-\sqrt{B}}=\sqrt{4}-\sqrt{3}=2-\sqrt{3}$