ANSWER
x = 65
EXPLANATION
To solve this equation, first, we have to subtract 3 from both sides,
[tex]\begin{gathered} \sqrt[]{x-1}+3-3=11-3 \\ \sqrt[]{x-1}=8 \end{gathered}[/tex]
Next, square both sides of the equation,
[tex]\begin{gathered} (\sqrt[]{x-1})^2=8^2 \\ x-1=64 \end{gathered}[/tex]
And finally, add 1 to both sides,
[tex]\begin{gathered} x-1+1=64+1 \\ x=65 \end{gathered}[/tex]
Hence, x = 65.
