Answer
$12-2\sqrt{11}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{11}-1)^2
,$ use the special product on squaring binomials and the properties of radicals. Then combine like terms.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{11})^2-2(\sqrt{11})(1)+(1)^2
\\\\=
11-2\sqrt{11}+1
.\end{array}
By combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(11+1)-2\sqrt{11}
\\\\=
12-2\sqrt{11}
.\end{array}
