Question
/1 Points] DETAILS Use the square root property to solve th \[ z^{2}-12=0 \]
Ask by Kirk Gibbs. in the United States
Nov 30,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( z_{1}=-2\sqrt{3}, z_{2}=2\sqrt{3} \)
Solution
Solve the equation \( z^{2}-12=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(z^{2}-12=0\)
- step1: Add or subtract both sides:
\(z^{2}=12\)
- step2: Simplify the expression:
\(z=\pm \sqrt{12}\)
- step3: Simplify the expression:
\(z=\pm 2\sqrt{3}\)
- step4: Separate into possible cases:
\(\begin{align}&z=2\sqrt{3}\\&z=-2\sqrt{3}\end{align}\)
- step5: Rewrite:
\(z_{1}=-2\sqrt{3},z_{2}=2\sqrt{3}\)
The solutions to the equation \(z^{2}-12=0\) using the square root property are \(z_{1}=-2\sqrt{3}\) and \(z_{2}=2\sqrt{3}\).
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Simplify this solution Beyond the Answer
To solve the equation \( z^{2} - 12 = 0 \) using the square root property, you can first isolate \( z^{2} \) by adding 12 to both sides. This gives you \( z^{2} = 12 \). Next, apply the square root to both sides: \( z = \pm \sqrt{12} \). Since \( \sqrt{12} \) can be simplified to \( 2\sqrt{3} \), your final solutions are \( z = 2\sqrt{3} \) and \( z = -2\sqrt{3} \). To check your work, simply substitute the values back into the original equation. For instance, plugging \( 2\sqrt{3} \) into \( z^{2} \) will yield \( (2\sqrt{3})^{2} = 12\), confirming that both values satisfy the equation. Happy calculating!
