Pregunta
Simplify. Assume \( m \) and \( n \) are greater than or equal to zero. \( 2 \sqrt{147 m n} \)
Ask by Phillips Lang. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The simplified expression is \(14\sqrt{3mn}\).
Solución
1. Write the expression:
\[
2 \sqrt{147mn}
\]
2. Factor \(147\) as \(147 = 49 \times 3\). Then, the expression becomes:
\[
2 \sqrt{49 \times 3mn}
\]
3. Use the property of square roots \(\sqrt{ab} = \sqrt{a}\sqrt{b}\):
\[
2 \sqrt{49} \sqrt{3mn}
\]
Since \(\sqrt{49} = 7\), we have:
\[
2 \times 7 \sqrt{3mn}
\]
4. Simplify the constant multiplication:
\[
14\sqrt{3mn}
\]
Thus, the simplified expression is:
\[
14\sqrt{3mn}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Beyond the Answer
To simplify \( 2 \sqrt{147 m n} \), we first break down the expression under the square root. The number \( 147 \) can be factored as \( 49 \times 3 \), where \( 49 \) is a perfect square. Thus, we have: \[ \sqrt{147 m n} = \sqrt{49 \times 3 \times m \times n} = \sqrt{49} \cdot \sqrt{3} \cdot \sqrt{m} \cdot \sqrt{n} = 7 \sqrt{3} \cdot \sqrt{m} \cdot \sqrt{n} \] Now we can multiply by the factor of \( 2 \): \[ 2 \sqrt{147 m n} = 2 \cdot 7 \sqrt{3} \sqrt{m} \sqrt{n} = 14 \sqrt{3mn} \] Thus, the simplified expression is: \[ \boxed{14 \sqrt{3mn}} \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
