Question

$\sqrt{x - 6} - 3 = 0$

Explanation:

Step1: Isolate the square root

Add 3 to both sides of the equation $\sqrt{x - 6}-3 = 0$ to get $\sqrt{x - 6}=3$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{x - 6}=3$. We know that $(\sqrt{a})^2=a$ for $a\geq0$, so squaring the left side gives $x - 6$, and squaring the right side gives $3^2 = 9$. So we have the equation $x-6 = 9$.

Step3: Solve for x

Add 6 to both sides of the equation $x - 6=9$. Then $x=9 + 6=15$.

Step4: Check the solution

Substitute $x = 15$ back into the original equation $\sqrt{15-6}-3=\sqrt{9}-3 = 3 - 3=0$, which satisfies the original equation.

Answer:

$x = 15$