Pregunta
Add the radical expressions. \[ 9 \sqrt{20}+2 \sqrt{45}=\square \] \( \sqrt{\square} \)
Ask by Vaughan Tran. in the United States
Jan 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The sum of the radical expressions \(9\sqrt{20}+2\sqrt{45}\) is \(24\sqrt{5}\).
Solución
Calculate or simplify the expression \( 9\sqrt{20}+2\sqrt{45} \).
Calculate the value by following steps:
- step0: Calculate:
\(9\sqrt{20}+2\sqrt{45}\)
- step1: Simplify the root:
\(9\times 2\sqrt{5}+2\sqrt{45}\)
- step2: Simplify the root:
\(9\times 2\sqrt{5}+2\times 3\sqrt{5}\)
- step3: Multiply the terms:
\(18\sqrt{5}+2\times 3\sqrt{5}\)
- step4: Multiply the terms:
\(18\sqrt{5}+6\sqrt{5}\)
- step5: Collect like terms:
\(\left(18+6\right)\sqrt{5}\)
- step6: Add the numbers:
\(24\sqrt{5}\)
The sum of the radical expressions \(9\sqrt{20}+2\sqrt{45}\) is \(24\sqrt{5}\).
Therefore, the answer is \(24\sqrt{5}\).
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Simplifique esta solución Beyond the Answer
To add the radical expressions, we first simplify each term. Starting with \( 9 \sqrt{20} \): \[ \sqrt{20} = \sqrt{4 \cdot 5} = 2 \sqrt{5}, \] so \[ 9 \sqrt{20} = 9 \cdot 2 \sqrt{5} = 18 \sqrt{5}. \] Now simplifying \( 2 \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \cdot 5} = 3 \sqrt{5}, \] therefore \[ 2 \sqrt{45} = 2 \cdot 3 \sqrt{5} = 6 \sqrt{5}. \] Adding them together: \[ 18 \sqrt{5} + 6 \sqrt{5} = (18 + 6) \sqrt{5} = 24 \sqrt{5}. \] Thus we have \[ 9 \sqrt{20} + 2 \sqrt{45} = 24 \sqrt{5}. \] So in the format given, \( \square = 24 \) and we find that \( \sqrt{\square} = \sqrt{24} = 2 \sqrt{6} \).
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