Pregunta
14. \( 2 \sqrt{48}-\sqrt{75}-\sqrt{12} \)
Ask by Peters Welch. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
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The simplified result is √3.
Solución
To simplify the expression 2√48 - √75 - √12, follow these steps:
1. Express each square root in its simplest form:
• √48 = √(16×3) = 4√3
• √75 = √(25×3) = 5√3
• √12 = √(4×3) = 2√3
2. Substitute these back into the original expression:
2√48 - √75 - √12 = 2(4√3) - 5√3 - 2√3
3. Simplify by multiplying and combining like terms:
2(4√3) = 8√3
So, 8√3 - 5√3 - 2√3 = (8 - 5 - 2)√3 = 1√3 = √3
The simplified result is √3.
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Simplifique esta solución The Deep Dive
First, let's simplify each term: 1. \( 2 \sqrt{48} = 2 \sqrt{16 \times 3} = 2 \times 4 \sqrt{3} = 8 \sqrt{3} \) 2. \( \sqrt{75} = \sqrt{25 \times 3} = 5 \sqrt{3} \) 3. \( \sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3} \) Now we can substitute these back into the original expression: \[ 2 \sqrt{48} - \sqrt{75} - \sqrt{12} = 8 \sqrt{3} - 5 \sqrt{3} - 2 \sqrt{3} \] Combine the like terms: \[ = (8 - 5 - 2) \sqrt{3} = 1 \sqrt{3} \] Thus, the simplified expression is: \[ \sqrt{3} \]
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