Pregunta
Find the real-number root. \[ \sqrt[5]{243} \] Write your answer in simplified form. Submit
Ask by Hamilton Sandoval. in Mexico
Mar 03,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The real-number root of 243 is 3.
Solución
We need to find the fifth root of 243, which can be written as
⁵√243.
Notice that 243 can be expressed as a power of 3 since 3⁵ = 243. Therefore,
⁵√243 = ⁵√(3⁵).
Taking the fifth root of 3⁵ gives
(3⁵)^(1/5) = 3^(5×1/5) = 3¹ = 3.
Thus, the simplified form of the real-number root is 3.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
The expression \( \sqrt[5]{243} \) can be simplified by recognizing that \( 243 \) can be expressed as \( 3^5 \). Therefore, we have: \[ \sqrt[5]{243} = \sqrt[5]{3^5} \] Applying the property of exponents that \( \sqrt[n]{a^n} = a \), we find: \[ \sqrt[5]{3^5} = 3 \] Thus, the real-number root is \[ \boxed{3} \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
