Select the correct classifications for √ 32.

Question

(rational, irrational) number

(repeating, nonrepeating, terminating) decimal

Answer 1

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

1. Rational or Irrational:
   The square root of 32 can be simplified as follows: \[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \] Since \( \sqrt{2} \) is an irrational number, \( 4\sqrt{2} \) is also irrational. Therefore, \( \sqrt{32} \) is an irrational number.

2. Repeating, Non-repeating, or Terminating Decimal:
   Since \( \sqrt{32} \) is irrational, it cannot be expressed as a decimal that terminates or repeats. Therefore, the decimal representation of \( \sqrt{32} \) is nonrepeating.

In summary:

• \( \sqrt{32} \) is an irrational number.
• The decimal representation of \( \sqrt{32} \) is nonrepeating.