Question

solve for z.
81 = z²
z = or
submit

Explanation:

Step1: Take square root of both sides

To solve for \( z \) in the equation \( 81 = z^2 \), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution because \( (\pm a)^2=a^2 \). So we have \( \sqrt{81}=\sqrt{z^2} \).

Step2: Simplify the square roots

We know that \( \sqrt{81} = 9 \) and \( \sqrt{z^2}=\vert z\vert \), but since we are solving for \( z \) in the equation \( z^2 = 81 \), the solutions are the values of \( z \) such that when squared give 81. So \( z=\pm\sqrt{81}=\pm 9 \).

Answer:

\( z = 9 \) or \( z = -9 \)