Question

What type of number will result from 512⋅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 evaluate \( 512 \cdot \sqrt{16} \):

1. Calculate \( \sqrt{16} \):
\[
\sqrt{16} = 4
\]

2. Now substitute this back into the original expression:
\[
512 \cdot \sqrt{16} = 512 \cdot 4
\]

3. Perform the multiplication:
\[
512 \cdot 4 = 2048
\]

The result, \( 2048 \), is a rational number.

Therefore, the correct response is:

**Rational because both factors are rational.**