Question

What type of number will result from $\frac {5}{12}\cdot \sqrt {16}$ ? (1 point)
Irrational, because both factors are irrational.
Rational, because both numbers are rational.
Radical, because one factor is a radical.
Irrational, because one factor is irrational.

Answer 1

To determine the type of number that results from the expression \(\frac{5}{12} \cdot \sqrt{16}\), we first evaluate the individual components of the expression:

1. **Evaluate \(\sqrt{16}\)**:
\[
\sqrt{16} = 4
\]

2. **Substituting back into the expression**:
\[
\frac{5}{12} \cdot 4
\]

3. **Perform the multiplication**:
\[
\frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12}
\]

4. **Simplifying the fraction**:
\[
\frac{20}{12} = \frac{5}{3}
\]

Now, we analyze the result, \(\frac{5}{3}\).

- The number \(5\) is an integer (which is a rational number).
- The number \(3\) is also an integer (which is a rational number).

Since both the numerator and the denominator are integers, the fraction \(\frac{5}{3}\) is a rational number.

Thus, the resulting type of number from the original expression \(\frac{5}{12} \cdot \sqrt{16}\) is:

\[
\boxed{\text{Rational, because both numbers are rational.}}
\]