Question

What type of number will result from 5/12⋅16−−√ ?(1 point) Responses 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. Radical, because one factor is a radical.

Answer 1

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

\[ \sqrt{16} = 4 \]

Now we substitute this back into the expression:

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

Next, we can multiply:

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

This can be simplified:

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

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

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