[tex]a)~~\sqrt{\sqrt{2} +1} \cdot \sqrt{\sqrt{2} -1} =\sqrt{(\sqrt{2} +1)\cdot (\sqrt{2} -1)} =\sqrt{(\sqrt{2} )^{2} -1^{2} } =\sqrt{2-1} =\sqrt{1} =1\\\\c)~~\sqrt{\sqrt{7} -\sqrt{3} } \cdot \sqrt{\sqrt{7} +\sqrt{3} } =\sqrt{(\sqrt{7} -\sqrt{3})\cdot (\sqrt{7} +\sqrt{3} ) } =\sqrt{(\sqrt{7} )^{2} -(\sqrt{3} )^{2} } =\sqrt{7-3} =\sqrt{4} =\sqrt{2^{2} } =2\\\\b)~~\sqrt{2+\sqrt{3} } \cdot \sqrt{2-\sqrt{3} }=\sqrt{(2+\sqrt{3})\cdot (2-\sqrt{3} ) }=\sqrt{2^{2} -(\sqrt{3} )^{2} } =\sqrt{4-3} =\sqrt{1} =1\\\\[/tex]
[tex]d)~~\sqrt{4-2\sqrt{3} } \cdot \sqrt{4+2\sqrt{3} }=\sqrt{(4-2\sqrt{3})\cdot (4+2\sqrt{3} ) }=\sqrt{4^{2} -(2\sqrt{3} )^{2} } =\sqrt{16-12} =\sqrt{4} =\sqrt{2^{2} } =2[/tex]
korzystam ze wzorów:
[tex]\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{x\cdot y} \\\\\sqrt[n]{x^{n} } =x^{n\cdot \frac{1}{n} } =x^{1} =x\\\\(x+y)\cdot (x-y)=x^{2} -y^{2}[/tex]
