Question

Choose which set or sets the following number belongs to. Be sure to account for ALL sets.
StartRoot 20 EndRoot
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Part 1
A.
irrational numbers
B.
real numbers
C.
rational numbers
D.
irrational​ numbers, real numbers
E.
rational​ numbers, real numbers

Answer 1

To determine which sets the number \( \sqrt{20} \) belongs to, let's analyze it step by step.

1. **Rational Numbers (Q)**: A number is rational if it can be expressed as a fraction of two integers, where the denominator is not zero. Since \( \sqrt{20} \) is not a perfect square, it cannot be expressed as a fraction of two integers. Therefore, it is not a rational number.

2. **Irrational Numbers (I)**: A number is classified as irrational if it cannot be expressed as a fraction of two integers. Since \( \sqrt{20} \) is not a perfect square, it is indeed an irrational number.

3. **Real Numbers (R)**: All rational and irrational numbers are considered real numbers. Thus, \( \sqrt{20} \) is also a real number.

Now, summarizing:

- \( \sqrt{20} \) is **irrational**.
- \( \sqrt{20} \) is also a **real** number.
- It is **not** a rational number.

Therefore, the correct response would be:

**D. irrational numbers, real numbers**