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 \( 512 \cdot \sqrt{16} \), we first recognize that \( \sqrt{16} = 4 \), which is a rational number.

Now, let's analyze the entire expression: \[ 512 \cdot \sqrt{16} = 512 \cdot 4 = 2048 \]

Since 2048 is a rational number, we can conclude that the expression results in a rational number.

The correct response is: Rational because one factor is a radical.