\( A = \left( {\sqrt {10} - \sqrt 2 } \right)\sqrt {3 + \sqrt 5 } \\ A = \sqrt {10\left( {3 + \sqrt 5 } \right)} - \sqrt {2\left( {3 + \sqrt 5 } \right)} \\ A = \sqrt {30 + 10\sqrt 5 } - \sqrt {6 + 2\sqrt 5 } \\ A = \sqrt {{{\left( {5 + \sqrt 5 } \right)}^2}} - \sqrt {{{\left( {1 + \sqrt 5 } \right)}^2}} \\ A = 5 + \sqrt 5 - \left( {1 + \sqrt 5 } \right)\\ A = 5 + \sqrt 5 - 1 - \sqrt 5 \\ A = 4 \)
\(A=\sqrt{2}\left(\sqrt{5}-1\right)\sqrt{\frac{6+2\sqrt{5}}{2}}\)
\(A=\) \(\left(\sqrt{5}-1\right)\sqrt{6+2\sqrt{5}}\)
\(A=\left(\sqrt{5}-1\right)\sqrt{\left(\sqrt{5}+1\right)^2}\)
\(A=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)\)
\(A=5+\sqrt{5}-\sqrt{5}-1\)
\(A=4\)
\(A=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3+\sqrt{5}}\)
=\(\sqrt{2}\left(\sqrt{5}-1\right)\sqrt{3+\sqrt{5}}\)
=\(\left(\sqrt{5}-1\right)\sqrt{6+2\sqrt{5}}\)
=\(\left(\sqrt{5}-1\right)\sqrt{1+2\sqrt{5}+5}\)
=\(\left(\sqrt{5}-1\right)\sqrt{\left(\sqrt{5}+1\right)^2}\)
=\(\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=\left(\sqrt{5}\right)^2-1^2\)
=\(5-1=4\)
