C,  41   39  37 bytes

s;
#define f(x).5/(s=sqrt(x))*(x+s*s)

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C,  49   47   45  43 bytes

s;float f(x){return.5/(s=sqrt(x))*(x+s*s);}

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Thanks to @JungHwan Min for saving two bytes!

C, 34 bytes

Thanks to @Olivier Grégoire!

s;
#define f(x)(x/(s=sqrt(x))+s)/2

Works only with float inputs.

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C,  41   39  37 bytes

s;
#define f(x).5/(s=sqrt(x))*(x+s*s)

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C,  49   47   45  43 bytes

s;float f(x){return.5/(s=sqrt(x))*(x+s*s);}

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Thanks to @JungHwan Min for saving two bytes!

C,  41  39 bytes

s;
#define f(x)(x+(s=sqrt(x))*s)/(2.*s)

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C,  49   47  45 bytes

s;float f(x){s=sqrt(x);return(x+s*s)/(2.*s);}

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Thanks to @JungHwan Min for saving two bytes!

C,  41   39  37 bytes

s;
#define f(x).5/(s=sqrt(x))*(x+s*s)

Try it online!

C,  49   47   45  43 bytes

s;float f(x){return.5/(s=sqrt(x))*(x+s*s);}

Try it online!

Thanks to @JungHwan Min for saving two bytes!

C, 41 bytes

s;
#define f(x)(x+(s=sqrt(x))*s)/(0.+s+s)

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C,  49  47 bytes

s;float f(x){s=sqrt(x);return(x+s*s)/(0.+s+s);}

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Thanks to @JungHwan Min for saving two bytes!

C,  41  39 bytes

s;
#define f(x)(x+(s=sqrt(x))*s)/(2.*s)

Try it online!

C,  49   47  45 bytes

s;float f(x){s=sqrt(x);return(x+s*s)/(2.*s);}

Try it online!

Thanks to @JungHwan Min for saving two bytes!