Pregunta
Evaluate the following radical. \( \sqrt[3]{125} \) a.) -5 b.) non-real solution c.) 5 d.) 25
Ask by Gray Lyons. in the United States
Jan 26,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The cube root of 125 is 5.
Solución
To evaluate \( \sqrt[3]{125} \), we need to find the real number that, when multiplied by itself three times (cubed), equals 125.
Let's break it down:
\[
\sqrt[3]{125} = x \quad \text{such that} \quad x^3 = 125
\]
We know that:
\[
5^3 = 5 \times 5 \times 5 = 125
\]
Therefore:
\[
\sqrt[3]{125} = 5
\]
**Answer:**
c.) 5
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Simplifique esta solución Bonus Knowledge
The expression \( \sqrt[3]{125} \) seeks to find a number that, when multiplied by itself three times, equals 125. In this case, \( 5 \times 5 \times 5 = 125 \). Thus, the answer is 5! Cubed roots can yield negative solutions as well, but in this case, \( \sqrt[3]{125} \) is simply 5 since we are looking for the principal root. Always a good idea to check your math!
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