+118724 There wasn't a balanced number of brackets so I added one at the end.
$$((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{-1/2}-(1-(2^{1/2})*((2-3^{1/2})^{1/2})^{1/2})\\\\
=((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{-1/2}-(1-(2^{1/2})(2-3^{1/2})^{1/4})\\\\
=\frac{1}{((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{1/2}}-(1-(2^{1/2})(2-3^{1/2})^{1/4})\\\\
=\dfrac{1}{\sqrt{\sqrt2 *\sqrt{(2-\sqrt3)}+3}}-\left(1-\sqrt2 \:\sqrt[4]{(2-\sqrt3}\:\right)\\\\$$
The site calcanswered what you wrote. I answered something closer to what you may have meant.
I doubt that it was a serious question anyway so it really doesn't matter. 
$${\left({\frac{\left({\frac{{{\mathtt{2}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\left({\mathtt{2}}{\mathtt{\,-\,}}{\frac{{{\mathtt{3}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}^{{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}}{\mathtt{\,-\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}{\frac{\left({\frac{{{\mathtt{2}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\left({\frac{{\left({\mathtt{2}}{\mathtt{\,-\,}}{\frac{{{\mathtt{3}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right) = -{\mathtt{0.320\: \!299\: \!803\: \!774\: \!770\: \!9}}$$
+118724 There wasn't a balanced number of brackets so I added one at the end.
$$((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{-1/2}-(1-(2^{1/2})*((2-3^{1/2})^{1/2})^{1/2})\\\\
=((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{-1/2}-(1-(2^{1/2})(2-3^{1/2})^{1/4})\\\\
=\frac{1}{((2^{1/2})*(2-3^{1/2})^{1/2}+3)^{1/2}}-(1-(2^{1/2})(2-3^{1/2})^{1/4})\\\\
=\dfrac{1}{\sqrt{\sqrt2 *\sqrt{(2-\sqrt3)}+3}}-\left(1-\sqrt2 \:\sqrt[4]{(2-\sqrt3}\:\right)\\\\$$
The site calcanswered what you wrote. I answered something closer to what you may have meant.
I doubt that it was a serious question anyway so it really doesn't matter.
$${\left({\frac{\left({\frac{{{\mathtt{2}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\left({\mathtt{2}}{\mathtt{\,-\,}}{\frac{{{\mathtt{3}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}^{{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}}{\mathtt{\,-\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}{\frac{\left({\frac{{{\mathtt{2}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\left({\frac{{\left({\mathtt{2}}{\mathtt{\,-\,}}{\frac{{{\mathtt{3}}}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right)}^{{\mathtt{1}}}}{{\mathtt{2}}}}\right) = -{\mathtt{0.320\: \!299\: \!803\: \!774\: \!770\: \!9}}$$
