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

Question

5
12
⋅
16
?(1 point)
Responses

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

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

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

Irrational, because both factors are irrational.
Irrational, because both factors are irrational.

Answer 1

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

\[ \sqrt{16} = 4 \]

Now substituting that back into the expression, we have:

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

Here, \( \frac{5}{3} \) is a rational number, as it can be expressed as a ratio of two integers (5 and 3).

Thus, the correct response is:

Rational, because both numbers are rational.