SOLUTION: how get sqrt(3+sqrt(5-sqrt(13+sqrt(48)))) show than (sqrt(2)+sqrt(6))/2 helpme please

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Question 1037220: how get sqrt(3+sqrt(5-sqrt(13+sqrt(48)))) show than (sqrt(2)+sqrt(6))/2
helpme please

Found 2 solutions by Alan3354, Rishikesh1501:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
how get sqrt(3+sqrt(5-sqrt(13+sqrt(48))))
Using a calculator, =~ 1.93185
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show than (sqrt(2)+sqrt(6))/2
Show what?

Answer by Rishikesh1501(1) (Show Source):
You can put this solution on YOUR website!
y=sqrt(3+sqrt(5-sqrt(13+sqrt(48))))
=sqrt(3+sqrt(5-sqrt(12+1+2sqrt(12))))
=sqrt(3+sqrt(5-sqrt(sqrt(12)+1)^2)))
=sqrt(3+sqrt(5-1-sqrt(12))
=sqrt(3+sqrt(4-sqrt(12))
=sqrt(3+sqrt(3+1-sqrt2(3))
=sqrt(3+sqrt(3)-1)
=sqrt(2+sqrt(3)) = sqrt(8+4.sqrt(3))/2=sqrt(6+2+2.sqrt(12))/2
=(sqrt(6)+sqrt(2))/2, Hence shown.