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.

Irrational, because one factor is irrational.
Irrational, because one factor is irrational.

Radical, because one factor is a radical.
Radical, because one factor is a radical.

Rational, because both numbers are rational.

Answer 1

To determine the type of number resulting from the expression \( \frac{5}{12} \cdot \sqrt{16} \), let's evaluate it step by step:

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

2. Multiply \( \frac{5}{12} \) by \( 4 \): \[ \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} \]

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

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

Based on the analysis, the correct response is:

Rational, because both numbers are rational.