What type of number will result from 5/12⋅ √16

Question

?(1 point)
Responses

Irrational, because both factors are irrational.
Irrational, because both factors are irrational.
Radical, because one factor is a radical.
Radical, because one factor is a radical.
Rational, because both numbers are rational.
Rational, because both numbers are rational.
Irrational, because one factor is irrational.

Answer 1

To determine the type of number that results from the expression \( \frac{5}{12} \cdot \sqrt{16} \), let's analyze the components:

1. Evaluate \( \sqrt{16} \): \[ \sqrt{16} = 4 \] This is a rational number.

2. Evaluate \( \frac{5}{12} \): \[ \frac{5}{12} \] This is also a rational number.

3. Multiply the two results: \[ \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3} \]

Now, \( \frac{5}{3} \) is a rational number.

Given these considerations, the correct answer is:

Rational, because both numbers are rational.