PDF or CDF of the sum of two Weibull random variables with shape parameter 1/2

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I saw that the pdf of the sum of two independent Weibull random variables is not known in general.

However, in the case of 'shape parameter = 1/2' in both variables, is there a closed-form expression of the pdf of the sum of two Weibull random variables?

Sum of two Weibull random variables with shape parameter = 1/2 is same with sum of two square of exponential random variables.

If not, can I calculate the probability of the sum of two Weibull random variables through Wolfram Alpha?