Infinity radicals

Algebra Level 5

the value of 5+152+32+38+3128+31282×2...\sqrt{5+\sqrt{\dfrac{15}{2}+\sqrt{\dfrac{3}{2}+\sqrt{\dfrac{3}{8}+\sqrt{\dfrac{3}{128}+\sqrt{\dfrac{3}{128^2 \times 2}...\infty}}}}}} can be expressed as n\sqrt{n}. find n this is part of the set the Radicals

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