Question

solve for z.
3 = \sqrt{z - 2}
z = \square
submit

Explanation:

Step1: Square both sides to eliminate the square root

To solve for \( z \) in the equation \( 3 = \sqrt{z - 2} \), we first square both sides of the equation. Squaring a square root will cancel out the square root operation. So, we have:
\[
3^2 = (\sqrt{z - 2})^2
\]

Step2: Simplify both sides

Simplifying the left side, \( 3^2 = 9 \). On the right side, \( (\sqrt{z - 2})^2 = z - 2 \) (since squaring a square root of a number gives the number itself, as long as the number inside the square root is non - negative, which we will check later). So now our equation is:
\[
9 = z - 2
\]

Step3: Solve for z

To solve for \( z \), we add 2 to both sides of the equation. Adding 2 to both sides gives:
\[
9 + 2 = z - 2 + 2
\]
Simplifying both sides, we get \( 11 = z \), or \( z = 11 \).

Step4: Check the solution (optional but recommended)

We substitute \( z = 11 \) back into the original equation \( 3=\sqrt{z - 2} \). The right - hand side becomes \( \sqrt{11 - 2}=\sqrt{9}=3 \), which is equal to the left - hand side. So the solution is valid.

Answer:

\( 11 \)