Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Irrational: √92 ≈ 9.59166.... It is irrational because it is the square root of an integer that is not a perfect square. All such square roots are irrational.

_____

Additional comment

In general, the n-th root of an integer that is not a perfect n-th power will be irrational. For example, ∛885 ≈ 9.600954766... is irrational, because 885 is not a perfect cube. (9³=729, 10³=1000)

Trig functions of (non-zero) rational angles in radians will be irrational. For example, tan(1.467) ≈ 9.5996286... is irrational.

Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational. (2 points) Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Respuesta :

A.

B.

Otras preguntas

Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)