Pregunta
Simplify the expression. (Assume that all variables are positive.) \[ 5 \sqrt{a b^{2}}-b \sqrt{a} \]
Ask by Powell Lynch. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The simplified expression is \(4b\sqrt{a}\).
Solución
To simplify the expression \( 5 \sqrt{a b^{2}} - b \sqrt{a} \), let's break it down step by step.
1. **Simplify \( \sqrt{a b^{2}} \):**
\[
\sqrt{a b^{2}} = \sqrt{a} \cdot \sqrt{b^{2}} = \sqrt{a} \cdot b = b \sqrt{a}
\]
2. **Substitute back into the original expression:**
\[
5 \sqrt{a b^{2}} - b \sqrt{a} = 5 \cdot (b \sqrt{a}) - b \sqrt{a}
\]
3. **Combine like terms:**
\[
5b \sqrt{a} - b \sqrt{a} = (5b - b) \sqrt{a} = 4b \sqrt{a}
\]
So, the simplified form of the expression is:
\[
4 b \sqrt{a}
\]
**Answer:** \(4\,b\,\sqrt{\,a\,}\)
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución The Deep Dive
To simplify the expression \( 5 \sqrt{a b^{2}} - b \sqrt{a} \), we can factor out the common term. First, note that \( \sqrt{a b^{2}} = \sqrt{a} \cdot \sqrt{b^{2}} = \sqrt{a} \cdot b \). Therefore, we can rewrite the first term: \[ 5 \sqrt{a b^{2}} = 5b \sqrt{a} \] Now, substitute this back into the expression: \[ 5b \sqrt{a} - b \sqrt{a} \] Next, factor out the common term \( b \sqrt{a} \): \[ b \sqrt{a} (5 - 1) = b \sqrt{a} \cdot 4 = 4b \sqrt{a} \] Thus, the simplified expression is: \[ \boxed{4b \sqrt{a}} \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
