Question

What type of number will result from 5/12 x square root of 16?
Irrational because one factor is irrational
Irrational because one factor is irrational

Irrational because both factors are irrational
Irrational because both factors are irrational

Rational because one factor is a radical
Rational because one factor is a radical

Rational because both factors are rational

Answer 1

To determine the type of number that results from the expression \( \frac{5}{12} \times \sqrt{16} \), let's evaluate it step by step.

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

2. **Multiply the fractions**:
\[
\frac{5}{12} \times 4 = \frac{5 \times 4}{12} = \frac{20}{12}
\]

3. **Simplify \( \frac{20}{12} \)**:
\[
\frac{20}{12} = \frac{5}{3}
\]

Now we have \( \frac{5}{3} \), which is a rational number. Therefore, the correct conclusion is:

**Rational because both factors are rational.**

In the context of the answer choices, the most fitting statement would be:

**Rational because one factor is a radical** (though this isn’t strictly accurate, this note relates to the fact that \( \sqrt{16} \) is indeed rational; however, the more specific answer not included in the options - that both inputs lead to a rational number would be accurate).