What type of number will result from 5/12 ⋅ √16 ?(1 point)

Question

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.

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Radical, because one factor is a radical.

Answer 1

To determine the type of number that will result from the expression \( \frac{5}{12} \cdot \sqrt{16} \), we can simplify it:

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

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

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

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

Since \( \frac{5}{3} \) is a fraction of two integers, it is a rational number.

Thus, the correct response is:

Rational, because both numbers are rational.