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

Question

?(1 point)
Responses

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

Answer 1

To determine the type of number resulting from the expression \( \frac{5}{12} \cdot \sqrt{16} \), we first need to evaluate the square root and then perform the multiplication.

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

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

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

4. The result \( \frac{5}{3} \) is a rational number because it can be expressed as the ratio of two integers.

Therefore, the correct response is: Rational, because both numbers are rational.