Question
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Answer
The simplified form is \(9\sqrt{2}\).
Solution
Calculate or simplify the expression \( 3\sqrt{8}-\sqrt{2}+\sqrt{32} \).
Calculate the value by following steps:
- step0: Calculate:
\(3\sqrt{8}-\sqrt{2}+\sqrt{32}\)
- step1: Simplify the root:
\(3\times 2\sqrt{2}-\sqrt{2}+\sqrt{32}\)
- step2: Simplify the root:
\(3\times 2\sqrt{2}-\sqrt{2}+4\sqrt{2}\)
- step3: Multiply the terms:
\(6\sqrt{2}-\sqrt{2}+4\sqrt{2}\)
- step4: Collect like terms:
\(\left(6-1+4\right)\sqrt{2}\)
- step5: Calculate:
\(9\sqrt{2}\)
The simplified form of the expression \(3\sqrt{8}-\sqrt{2}+\sqrt{32}\) is \(9\sqrt{2}\).
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Simplify this solution Beyond the Answer
Let's simplify the expression step by step. First, notice that \( \sqrt{32} \) can be simplified: \[ \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \] Now, substituting this into the original expression gives us: \[ 3 \sqrt{8} - \sqrt{2} + 4\sqrt{2} \] Next, we simplify \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \] Now, substitute \( \sqrt{8} \) back into the expression: \[ 3(2\sqrt{2}) - \sqrt{2} + 4\sqrt{2} \] This simplifies further to: \[ 6\sqrt{2} - \sqrt{2} + 4\sqrt{2} \] Now, combine the like terms: \[ (6 - 1 + 4)\sqrt{2} = 9\sqrt{2} \] So, the final result of the expression \( 3 \sqrt{8}-\sqrt{2}+\sqrt{32} \) is: \[ \boxed{9\sqrt{2}} \]
