Questions: What type of number will result from 5/12 * sqrt(16) ? (1 point) Irrational because one factor is irrational Irrational because both factors are irrational Rational because one factor is a radical Rational because both factors are rational

What type of number will result from 5/12 * sqrt(16) ?
(1 point)
Irrational because one factor is irrational
Irrational because both factors are irrational
Rational because one factor is a radical
Rational because both factors are rational

Transcript text: What type of number will result from $\frac{5}{12} \cdot \sqrt{16}$ ? (1 point) Irrational because one factor is irrational Irrational because both factors are irrational Rational because one factor is a radical Rational because both factors are rational

Solution

Solution Steps

To determine the type of number resulting from the given expression, we need to evaluate the expression and analyze the result. Specifically, we need to compute the product of $\frac{5}{12}$ and $\sqrt{16}$, and then determine if the result is rational or irrational.

Step 1: Evaluate $\sqrt{16}$

We start by calculating $\sqrt{16}$: \[ \sqrt{16} = 4 \]

Step 2: Calculate the Product

Next, we compute the product of $\frac{5}{12}$ and $4$: \[ \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3} \]

Step 3: Determine the Type of Number

The result $\frac{5}{3}$ is a fraction where both the numerator and denominator are integers. Therefore, it is a rational number.