SAT Mathematics Practice Test 5

If x = 9 in the equation $\sqrt{\mathit{k}+2}-\mathit{x}=0$ this equation becomes $\sqrt{\mathit{k}+2}-9=0$,which can be written as $\sqrt{\mathit{k}+2}-9$.Squaring each side of $\sqrt{\mathit{k}+2}=9$ gives $\mathit{k}+2=81$ or $\mathit{k}=79$ Substituting k = 79 into the equation $\sqrt{\mathit{k}+2}-9=0$ confirms this is the correct value for k.
Choices A, B, and C are incorrect because substituting any of these values for k in the equation $\sqrt{\mathit{k}+2}-9=0$ gives a false statement. For example, if $\mathit{k}=7$, the equation becomes $\sqrt{7+2}-9=\sqrt{9}-9=3-9=0$,which is false.