[tex]a)mg = \sqrt{ab} = \sqrt{( \sqrt{5} - 1)( \sqrt{5} + 1} )[/tex]
[tex]mg = \sqrt{ { (\sqrt{5}) }^{2} - {1}^{2} } [/tex]
[tex]mg = \sqrt{5 - 1} [/tex]
[tex]mg = \sqrt{4} [/tex]
[tex]mg = 1[/tex]
[tex]b)mg = \sqrt{ab} = \sqrt{( \sqrt{10} + 1)( \sqrt{10} - 1) } [/tex]
[tex] mg = \sqrt{ ({ \sqrt{10}) }^{2} - {1}^{2} } [/tex]
[tex]mg = \sqrt{10 - 1} [/tex]
[tex]mg = \sqrt{9} [/tex]
[tex]mg = 3[/tex]
[tex]c)mg = \sqrt{ab} = \sqrt{( \sqrt{11} + \sqrt{2} )( \sqrt{11} - \sqrt{2} )} [/tex]
[tex]mg = \sqrt{ ({ \sqrt{11} )}^{2} - { (\sqrt{2} )}^{2} } [/tex]
[tex]mg = \sqrt{11 - 2} [/tex]
[tex]mg = \sqrt{9} [/tex]
[tex]mg = 3[/tex]
[tex]d)mg = \sqrt{ab} = \sqrt{(3 \sqrt{3} - 5)(3 \sqrt{3} + 5)} [/tex]
[tex]mg = \sqrt{ ({3 \sqrt{3}) }^{2} - {5}^{2} } [/tex]
[tex]mg = \sqrt{27 - 25} [/tex]
[tex]mg = \sqrt{2} [/tex]