Question

What type of number will result from 5/12⋅16−−√ ?(1 point) Responses Rational, because both numbers are rational. Rational, because both numbers are rational. 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. Irrational, because both factors are irrational. Irrational, because both factors are irrational.

Answer 1

To determine the type of number that results from the expression \( \frac{5}{12} \cdot \sqrt{16} \), let's break it down:

1. Evaluate \( \sqrt{16} \): \(\sqrt{16} = 4\), which is a rational number.

2. Calculate the product \( \frac{5}{12} \cdot 4 \): \[ \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3}. \]

The result \( \frac{5}{3} \) is a rational number.

Now looking at the provided response options, the correct one is:

Rational, because both numbers are rational.