Answer
$(\sqrt{x-1}+5)^{2}=x+10\sqrt{x-1}+24$
Work Step by Step
$(\sqrt{x-1}+5)^{2}$
Use the formula for squaring a binomial to evaluate this power. The formula is $(a+b)^{2}=a^{2}+2ab+b^{2}$. In this expression, $a=\sqrt{x-1}$ and $b=5$.
Substitute the known values into the formula and simplify:
$(\sqrt{x-1}+5)^{2}=(\sqrt{x-1})^{2}+10\sqrt{x-1}+25=...$
$...=x-1+10\sqrt{x-1}+25=x+10\sqrt{x-1}+24$
