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.

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

Rational, because both numbers are rational.

Answer 1

To evaluate the expression \( \frac{5}{12} \cdot \sqrt{16} \), we first simplify \( \sqrt{16} \).

\[ \sqrt{16} = 4 \]

Now we can substitute this back into the expression:

\[ \frac{5}{12} \cdot 4 \]

Next, we multiply \( \frac{5}{12} \) by \( 4 \):

\[ \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3} \]

The resulting number, \( \frac{5}{3} \), is a rational number. Thus, the correct response is:

Rational, because both numbers are rational.