[Python] Root mean square linearisation for linear programming

I am trying to linearise the function root mean square to use it in a linear optimisation or Mixed integer linear optimisation. Any idea how I could do this? For instance with the example below, if I wanted to maximize P*100, the model would give P=10, Q = 0 and S=10.

Many thanks

import numpy as np
import pulp

S = np.sqrt(P**2 + Q**2)

model = pulp.LpProblem("Linearise RMS", pulp.LpMaximize)

P = pulp.LpVariable("P", lowBound=-10, upBound=10 ,cat="Continuous")
Q = pulp.LpVariable("Q", lowBound=-10, upBound=10 ,cat="Continuous")
S = pulp.LpVariable("S", lowBound= 0, upBound=10 ,cat="Continuous")

objective_function = P*100

model.setObjective(objective_function)
cbc_solver = PULP_CBC_CMD(options=['ratioGap=0.02'])
result = model.solve(solver=cbc_solver)

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