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

Question

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(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.