Maximum value is not as big as you think

Algebra Level 5

ab2c3d4\large a\sqrt [ 2 ]{ b } \sqrt [ 3 ]{ c } \sqrt [ 4 ]{ d }

If a,b,c,d>0a,b,c,d > 0 which satisfy the equation: 36a+4b+4c+3d=2536a+4b+4c+3d=25, find the maximum value of the expression above.

Give your answer to 3 decimal places.

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