Question: How to obtain this simplification in Maple for x<=0

Any one has a trick to show in Maple that  x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4; is zero for x<=0?

I'd like to get similar simplication as this below but in Maple, But everything I tried so far did not work. I am sure there is a way in Maple, but have not found it yet.

Below is the Maple worksheet

interface(version)

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

restart;

r := x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4;

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r,symbolic) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

simplify(r,sqrt) assuming x<0

x+(1/4)*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2)

#showing it is zero for x<=0
plot(r,x=-10..1)

 

Download show_it_is_zero.mw

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