Question

The value of $\left|\sqrt{4+2\sqrt{3}}\right|-\left|\sqrt{4-2\sqrt{3}}\right|$ is

• A. 1
• B. 2
• C. 4
• D. 3
• E. 5

Answer 1

Answer: (B)

We have,
$|\sqrt{4+2\sqrt{3}}|-|\sqrt{4-2\sqrt{3}}|$
$=|\sqrt{3+1+2\sqrt{3}}|-|\sqrt{3+1-2\sqrt{3}}|$
$=\left|\sqrt{(\sqrt{3}{)}^2+(1{)}^2+2\cdot \sqrt{3}\cdot 1}\right|$
$-\mid \sqrt{(\sqrt{3}{)}^2+(1{)}^2-2\cdot \sqrt{3}\cdot 1\mid }$
$=\left|\sqrt{(\sqrt{3}+1{)}^2}\right|-\mid \sqrt{(\sqrt{3})-1{)}^2\mid }$
$=|\sqrt{3}+1|-|\sqrt{3}-1|$
$=(\sqrt{3}+1)-(\sqrt{3}-1)=2$