Identify whether each number is rational or irrational. Justify your answer. a. √25

• Rational, because it is a perfect square and equals 5.

• Irrational, because it cannot be expressed as a fraction.

• Rational, because it is an infinite non-repeating decimal.

• Irrational, because it is a fraction.

Identify whether each number is rational or irrational. Justify your answer. b. √21 / √7

• Rational, because it simplifies to √3 which is a perfect square.

• Irrational, because it simplifies to √3 which is not a perfect square.

• Rational, because it is a fraction.

• Irrational, because it is a non-terminating decimal.

Identify whether each number is rational or irrational. Justify your answer. c. π

• Rational, because it can be expressed as a fraction.

• Irrational, because it is a non-terminating, non-repeating decimal.

• Rational, because it is a perfect square.

• Irrational, because it is a fraction.

Tags

CCSS.8.NS.A.1

Identify whether each number is rational or irrational. Justify your answer. d. √8 / √18

• Rational, because it simplifies to a fraction.

• Irrational, because it simplifies to a non-terminating decimal.

• Rational, because it simplifies to 2√2 / 3√2 which equals 2/3.

• Irrational, because it simplifies to 2√2 / 3√2 which is not a perfect square.

Tags

CCSS.HSN.RN.B.3

Identify whether each number is rational or irrational. Justify your answer. e. 2/9

• Rational, because it is a fraction with integer numerator and denominator.

• Irrational, because it is a non-terminating decimal.

• Rational, because it is a non-repeating decimal.

• Irrational, because it cannot be expressed as a fraction.

Identify whether each number is rational or irrational. Justify your answer. f. 17/29

• Rational, because it is a fraction with integer numerator and denominator.

• Irrational, because it is a non-terminating decimal.

• Rational, because it is a non-repeating decimal.

• Irrational, because it cannot be expressed as a fraction.

The diameter of a circle is 14 cm. The circumference is 43.9823 cm. Use the formula C = πd to approximate the value of π to 8 decimal places.