Question
Solve for \( x \) using the square root property. \( n^{2}-6=0 \) \( n= \) Entry Tip: Do not use a decimal approximation for square roots. To enter a number like \( 5 \sqrt{7} \), type \( 5^{*} \) sqrt(7). Preview your answer before submitting! Furthere Tip: Write your answers as a list, with your answers separated by (a) comma(s). For example, if you get 4 and \( -\frac{2}{3} \) as your answers, then enter \( 4,-2 / 3 \) in the box.
Ask by Brewer Montgomery. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( n = -\sqrt{6}, \sqrt{6} \)
Solution
Solve the equation \( n^{2}-6=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(n^{2}-6=0\)
- step1: Add or subtract both sides:
\(n^{2}=6\)
- step2: Simplify the expression:
\(n=\pm \sqrt{6}\)
- step3: Separate into possible cases:
\(\begin{align}&n=\sqrt{6}\\&n=-\sqrt{6}\end{align}\)
- step4: Rewrite:
\(n_{1}=-\sqrt{6},n_{2}=\sqrt{6}\)
The solutions to the equation \( n^{2}-6=0 \) using the square root property are \( n = -\sqrt{6} \) and \( n = \sqrt{6} \).
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Simplify this solution Extra Insights
To solve the equation \( n^{2}-6=0 \) using the square root property, we first isolate \( n^{2} \): \[ n^{2} = 6 \] Next, we apply the square root property, which gives us: \[ n = \pm \sqrt{6} \] Thus, the solutions are: \[ n = \sqrt{6}, -\sqrt{6} \] So, the final answer is: \[ \sqrt{6},-\sqrt{6} \]
