Pregunta
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 3 \sqrt{864} = 36\sqrt{6} \)
Solución
To simplify the expression \( 3 \sqrt{864} \), follow these steps:
1. **Factorize 864 into its prime factors:**
\[
864 = 2^5 \times 3^3
\]
2. **Simplify the square root using the prime factors:**
\[
\sqrt{864} = \sqrt{2^5 \times 3^3} = \sqrt{(2^4 \times 2) \times (3^2 \times 3)} = \sqrt{2^4} \times \sqrt{3^2} \times \sqrt{2 \times 3} = 2^2 \times 3^1 \times \sqrt{6} = 4 \times 3 \times \sqrt{6} = 12\sqrt{6}
\]
3. **Multiply by 3:**
\[
3 \sqrt{864} = 3 \times 12\sqrt{6} = 36\sqrt{6}
\]
**Final Answer:**
\[
3 \sqrt{864} = 36\sqrt{6}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución The Deep Dive
Did you know that \( \sqrt{864} \) can be simplified? It breaks down into \( \sqrt{144 \times 6} \), where \( \sqrt{144} \) equals 12. So, \( 3 \sqrt{864} = 3 \times 12 \sqrt{6} = 36 \sqrt{6} \). You just turned a complicated square root into a more manageable expression! Now imagine applying this knowledge in real-world situations. If you're an engineer needing precise measurements or an architect tackling spatial designs, being able to simplify square roots helps to make calculations faster and more accurate. That way, you can spend less time on math and more on building awesome structures!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
