Golden Root

Algebra Level 2

5 + 5 + 3 + 5 + 14 + 180 = ? \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{14 + \sqrt{180}}}} = \ ?

3 5 + 1 \sqrt{5} + 1 3 + 1 \sqrt{3} + 1 3 − 1 \sqrt{3} - 1 5 − 1 \sqrt{5} - 1

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A Former Brilliant Member by A Former Brilliant Member

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1 solution

5 + 5 + 3 + 5 + 14 + 180 \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{14 + \sqrt{180}}}} = 5 + 5 + 3 + 5 + ( 5 + 3 ) 2 = \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{(\sqrt{5}+3)^2}}} = 5 + 5 + 3 + 5 + 5 + 3 = \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{5} + 3}} = 5 + 5 + 6 + 2 5 = 5 + 5 + ( 5 + 1 ) 2 = \sqrt{5 + \sqrt{5} + \sqrt{6+2\sqrt{5}}} = \sqrt{5 + \sqrt{5} + \sqrt{(\sqrt{5}+1)^2}} = 5 + 5 + 5 + 1 = 6 + 2 5 = \sqrt{5 + \sqrt{5} + \sqrt{5}+1}=\sqrt{6+2\sqrt{5}} = 5 + 1 =\sqrt{5}+1

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Wish I could upvote your solution twice.... Perfect!

Also.. Pls dont forget to submit your entry in BROW

Mehul Arora - 6 years, 3 months ago

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Thanks Mehul ,
and I submitted my entry in BROW also

A Former Brilliant Member - 6 years, 3 months ago

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Please submit a riddle >.<

Mehul Arora - 6 years, 3 months ago

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