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I got a solution in the form of a Root object from an equation:

y = Root[-1.1292882469618184`*^35 N^3 + 
    3.327201082265235`*^35 N^2 #1 - 
    3.2676236770106753`*^35 N #1^2 + (1.0697043581639466`*^35 + 
       4.055934940208895`*^29 N^2) #1^3 + 
    8.11186988041779`*^29 N #1^4 + 4.055934940208895`*^29 #1^5 &, 1]

which can be evaluated when I substitute the variable N with some number between 1 and 3:

y /. N -> 1
0.993688

However, I am not able to make Mathematica plot y in the range of [1,3]:

Plot[y, {N, 1, 3}]

The error message is "Limiting value 1 in {N,1,3} is not a machine-sized real number".

So what is the problem here and how can I solve it?

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Don't use N as a symbolname, because it's a predefined Mathematica function!

Try

y = Root[-1.1292882469618184`*^35 N^3 + 3.327201082265235`*^35 N^2 #1 -3.2676236770106753`*^35 N #1^2 + (1.0697043581639466`*^35 +4.055934940208895`*^29 N^2) #1^3 + 8.11186988041779`*^29 N #1^4 + 4.055934940208895`*^29 #1^5 &, 1] /. N -> n;
Plot[y ,{n,1,3}]

enter image description here

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