Select the correct classification for \sqrt(32)

Question

_ Number (Rational, Irrational)
_ Decimal (Repeating, Nonrepeating, Terminating)

Answer 1

To classify \(\sqrt{32}\):

1. Is it a Rational or Irrational Number?

   • \(\sqrt{32}\) can be simplified. We know that \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\). Since \(\sqrt{2}\) is an irrational number, \(4\sqrt{2}\) is also irrational. Therefore, \(\sqrt{32}\) is classified as an Irrational Number.

2. Is it a Decimal (Repeating, Nonrepeating, Terminating)?

   • Since \(\sqrt{32}\) is irrational, its decimal representation is nonterminating and nonrepeating. Thus, it is classified as a Nonrepeating Decimal.

In summary:

• Number: Irrational
• Decimal: Nonrepeating