\(=\dfrac{\sqrt{2}\sqrt{2-\sqrt{3}}}{\sqrt{2}}-\dfrac{\sqrt{2}\sqrt{2+\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}-\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}=\dfrac{\left|\sqrt{3}-1\right|-\left|\sqrt{3}+1\right|}{\sqrt{2}}=\dfrac{\sqrt{3}-1-\sqrt{3}-1}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
`= (sqrt (4 - 2 sqrt 3))/(sqrt 2) - (sqrt (4 + 2 sqrt 3))/(sqrt 2)`
`= (sqrt 3 - 1)/(sqrt 2) - (sqrt 3 +1)/(sqrt 2)`
`= (sqrt 3 - 1 - sqrt 3 - 1)/(sqrt 2)`
`= -2/sqrt 2 = - sqrt 2`
\(\sqrt{\left(2-\sqrt{3}\right)}-\sqrt{\left(2+\sqrt{3}\right)}\)
\(=\sqrt{\left(2^2-\sqrt{3}^2\right)}\)
=\(\sqrt{\left(4-3\right)}\)
\(=\sqrt{1}\)
= 1
