What type of number will result from 512⋅16−−√

Question

?(1 point)
Responses

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.

Rational, because both numbers are rational.

Answer 1

To determine the type of number that results from \( 512 \cdot \sqrt{16} \), let's analyze each component:

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

2. Calculating \(512 \cdot \sqrt{16}\): \[ 512 \cdot 4 = 2048 \] Since 2048 is also a rational number.

Now, we can analyze the options given:

• Irrational, because one factor is irrational. (not correct; both factors are rational)
• Radical, because one factor is a radical. (not the appropriate definition; the result is not classified as "radical")
• Irrational, because both factors are irrational. (not correct; both factors are rational)
• Rational, because both numbers are rational. (correct; both factors \(512\) and \(4\) are rational)

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