Upper bound for $(1+x)^{1/2}$ where $x>0$

Question

I am trying to find an upper bound, which is an algebraic function in $x$, for $(1+x)^{1/2}$ for $x>0$.

Note that $x$ need not be less than $1$. Binomial expansion can be used if $x<1$ but here $x$ can be an arbitrary positive real number. Any ideas?

Answer 1

$(1+x)^{1/2} \le 1+x^{1/2}$ for $x\ge 0$, as is verified by squaring.