Question-43349

Question Number 43349 by peter frank last updated on 10/Sep/18

Answered by math1967 last updated on 10/Sep/18

\sqrt{2 + \sqrt{5} - \sqrt{6 - 3 \sqrt{5} + \sqrt{(3 - \sqrt{{5)}^{2}}}}}

\sqrt{2 + \sqrt{5} - \sqrt{6 - 3 \sqrt{5} + 3 - \sqrt{5}}}

\sqrt{2 + \sqrt{5} - \sqrt{{(\sqrt{5} - 2)}^{2}}}

\sqrt{2 + \sqrt{5} - \sqrt{5} + 2}

\sqrt{4} = 2 (p r o v e d)

Commented by peter frank last updated on 10/Sep/18

m u c h r e s p e c t

Answered by Joel578 last updated on 10/Sep/18

\sqrt{14 - 6 \sqrt{5}} = \sqrt{14 - 2 \sqrt{45}} = 3 - \sqrt{5}

\sqrt{6 - 3 \sqrt{5} + 3 - \sqrt{5}} = \sqrt{9 - 4 \sqrt{5}} = \sqrt{9 - 2 \sqrt{20}}

= \sqrt{5} - 2

\sqrt{2 + \sqrt{5} - \sqrt{5} + 2} = \sqrt{4} = 2

Commented by malwaan last updated on 10/Sep/18

3 - \sqrt{5} ? ?

Commented by Joel578 last updated on 10/Sep/18

{(3 - \sqrt{5})}^{2} = 9 - 6 \sqrt{5} + 5 = 14 - 6 \sqrt{5} = 14 - 2 \sqrt{45}

\sqrt{{(3 - \sqrt{5})}^{2}} = \sqrt{14 - 2 \sqrt{45}}

Commented by peter frank last updated on 10/Sep/18

t h a n k s