Which of the following is not an irrational number?



A. \sqrt[5]{125}

B. \sqrt[4]{125}

C. \sqrt[4]{125}

D. \sqrt[6]{125}

E. \sqrt[3]{125}

To determine which of the following is not an irrational number, let's evaluate each expression:

### A. \(\sqrt[5]{125}\)
\[
\sqrt[5]{125} = \sqrt[5]{5^3}
\]
\[
= 5^{3/5}
\]
This is not an integer and thus is an irrational number.

### B. \(\sqrt[4]{125}\)
\[
\sqrt[4]{125} = \sqrt[4]{5^3}
\]
\[
= 5^{3/4}
\]
This is not an integer and thus is an irrational number.

### C. \(\sqrt[4]{125}\) (same as B)
\[
\sqrt[4]{125} = \sqrt[4]{5^3}
\]
\[
= 5^{3/4}
\]
This is not an integer and thus is an irrational number.

### D. \(\sqrt[6]{125}\)
\[
\sqrt[6]{125} = \sqrt[6]{5^3}
\]
\[
= 5^{3/6}
\]
\[
= 5^{1/2}
\]
This is the square root of 5, which is not an integer and thus is an irrational number.

### E. \(\sqrt[3]{125}\)
\[
\sqrt[3]{125} = \sqrt[3]{5^3}
\]
\[
= 5
\]
This is an integer and thus is a rational number.

Therefore, the correct answer is:

**E. \(\sqrt[3]{125}\)**

Would you like more details or have any questions? Here are some related questions for further practice:

1. Which of the following is an irrational number: \(\sqrt{16}\), \(\sqrt{20}\), \(\sqrt{25}\), \(\sqrt[3]{8}\)?
2. Determine if \(\sqrt[5]{32}\) is rational or irrational.
3. Simplify \(\sqrt[3]{64}\) and state if it is rational or irrational.
4. What is the cube root of 27? Is it rational or irrational?
5. Is \(\sqrt[4]{81}\) a rational number?
6. Evaluate \(\sqrt[3]{216}\) and determine its nature.
7. Find if \(\sqrt[4]{256}\) is rational or irrational.
8. Calculate \(\sqrt[5]{32}\) and state its nature.

**Tip:** A number is rational if it can be expressed as the quotient of two integers, and it is an integer if it is a whole number.

Learn how to identify irrational numbers by evaluating square roots of 125. This problem covers key concepts in number theory, including square roots, irrational numbers, and rational numbers. Suitable for students in Grades 7-9.

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