Question
9. \( 5 \sqrt{98}-3 \sqrt{6} \cdot 5 \sqrt{3} \)
Ask by Knight Bowman. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \(-10\sqrt{2}\).
Solution
Calculate or simplify the expression \( 5\sqrt{98}-3\sqrt{6}\cdot 5\sqrt{3} \).
Calculate the value by following steps:
- step0: Calculate:
\(5\sqrt{98}-3\sqrt{6}\times 5\sqrt{3}\)
- step1: Simplify the root:
\(5\times 7\sqrt{2}-3\sqrt{6}\times 5\sqrt{3}\)
- step2: Multiply the terms:
\(35\sqrt{2}-3\sqrt{6}\times 5\sqrt{3}\)
- step3: Multiply:
\(35\sqrt{2}-45\sqrt{2}\)
- step4: Collect like terms:
\(\left(35-45\right)\sqrt{2}\)
- step5: Subtract the numbers:
\(-10\sqrt{2}\)
The simplified form of \(5\sqrt{98}-3\sqrt{6}\cdot 5\sqrt{3}\) is \(-10\sqrt{2}\).
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Simplify this solution The Deep Dive
First, simplify \( 5 \sqrt{98} \). Since \( \sqrt{98} = \sqrt{49 \cdot 2} = 7\sqrt{2} \), we have: \[ 5 \sqrt{98} = 5 \cdot 7 \sqrt{2} = 35 \sqrt{2} \] Next, simplify \( -3 \sqrt{6} \cdot 5 \sqrt{3} \): \[ -3 \sqrt{6} \cdot 5 \sqrt{3} = -15 \sqrt{6 \cdot 3} = -15 \sqrt{18} \] Now simplify \( \sqrt{18} = \sqrt{9 \cdot 2} = 3 \sqrt{2} \), leading to: \[ -15 \sqrt{18} = -15 \cdot 3 \sqrt{2} = -45 \sqrt{2} \] Now combine the two terms: \[ 35 \sqrt{2} - 45 \sqrt{2} = (35 - 45) \sqrt{2} = -10 \sqrt{2} \] So the final answer is: \[ -10 \sqrt{2} \]
