1.

Question

What type of number will result from 5/12⋅sqr root 16
?

(1 point)
Responses

Irrational because one factor is irrational
Irrational because one factor is irrational

Irrational because both factors are irrational
Irrational because both factors are irrational

Rational because one factor is a radical
Rational because one factor is a radical

Rational because both factors are rational

Answer 1

To determine the type of number that results from the expression \( \frac{5}{12} \cdot \sqrt{16} \), we need to evaluate the components of the expression:

1. Calculate \( \sqrt{16} \): \[ \sqrt{16} = 4 \] (which is a rational number).

2. Evaluate the expression: \[ \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3} \] (which is also a rational number).

Since both factors in the original expression (\( \frac{5}{12} \) which is rational, and \( \sqrt{16} \) which is also rational) are rational, the product is also rational.

Therefore, the correct response is:

Rational because both factors are rational.