Question
assignment \( \leftarrow \quad \) Solve the quadratic equation \( r^{2}=8 \).
Ask by Weston Greene. in the United States
Mar 14,2025
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Answer
The solutions are \( r = -2\sqrt{2} \) and \( r = 2\sqrt{2} \).
Solution
Solve the equation \( r^{2}=8 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(r^{2}=8\)
- step1: Simplify the expression:
\(r=\pm \sqrt{8}\)
- step2: Simplify the expression:
\(r=\pm 2\sqrt{2}\)
- step3: Separate into possible cases:
\(\begin{align}&r=2\sqrt{2}\\&r=-2\sqrt{2}\end{align}\)
- step4: Rewrite:
\(r_{1}=-2\sqrt{2},r_{2}=2\sqrt{2}\)
The solutions to the quadratic equation \(r^{2}=8\) are \(r=-2\sqrt{2}\) and \(r=2\sqrt{2}\).
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Simplify this solution Mind Expander
To solve the equation \( r^{2} = 8 \), we can take the square root of both sides. Remember that taking the square root can yield both positive and negative results. So, we get: \( r = \sqrt{8} \) or \( r = -\sqrt{8} \). We can simplify \( \sqrt{8} \) further: \( \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \). Thus, the two solutions for the equation are: \( r = 2\sqrt{2} \) and \( r = -2\sqrt{2} \).
