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

?
Responses

Rational, because both numbers are rational.
Rational, because both numbers are rational. - not selected, this is the correct answer why is this the correct answer?

Irrational, because both factors are irrational.
Irrational, because both factors are irrational. - no response given

Radical, because one factor is a radical.
Radical, because one factor is a radical. - no response given

Irrational, because one factor is irrational.

give me two simple sentences

3 answers

The expression \( 512 \cdot \sqrt{16} \) equals \( 512 \cdot 4 \), which simplifies to 2048. Since both 512 and \( \sqrt{16} \) are rational numbers, their product is also rational.

What type of number will result from
5/12


√16
?
Responses

Rational, because both numbers are rational.
Rational, because both numbers are rational. - not selected, this is the correct answer

Irrational, because both factors are irrational.
Irrational, because both factors are irrational. - no response given

Radical, because one factor is a radical.
Radical, because one factor is a radical. - no response given

Irrational, because one factor is irrational.

The expression \( \frac{5}{12} \cdot \sqrt{16} \) simplifies to \( \frac{5}{12} \cdot 4 \), which equals \( \frac{20}{12} \) or \( \frac{5}{3} \). Since both \( \frac{5}{12} \) and \( \sqrt{16} \) (which is 4) are rational numbers, their product is also rational.

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