Which numbers are rational? Check the three that apply.

Question

Responses

\/104

pi

\/16

\/21

7/23

3.8

Answer 1

To determine which numbers are rational, recall that a rational number is any number that can be expressed as the quotient or fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Now, let's evaluate the given options:

1. $\sqrt{104}$: This is an irrational number because it cannot be simplified into a fraction of two integers.

2. $\pi$: This is also an irrational number and cannot be expressed as a fraction.

3. $\sqrt{16}$: This simplifies to 4, a whole number, which is rational (since it can be expressed as $\frac{4}{1}$).

4. $\sqrt{21}$: This is an irrational number because it cannot be simplified into a fraction of two integers.

5. $\frac{7}{23}$: This is a fraction of two integers, making it a rational number.

6. 3.8: This can be expressed as $\frac{38}{10}$ or $\frac{19}{5}$, thus it is also a rational number.

The three numbers that are rational from the given options are:

• $\sqrt{16}$
• $\frac{7}{23}$
• 3.8