Real numbers and irrational estimates

Answer: √2

1. √2 cannot be expressed as a ratio of integers. A terminating decimal, a fraction and √49=7 are rational.

Answer: π is irrational; 3.14 is a rational approximation

1. π has a non-terminating, non-recurring decimal expansion. The finite decimal 3.14 is only an approximation.

Answer: 12

1. 122=144<157<169=132, so the smaller bounding integer is 12.