Question

The square root of 19 is an irrational number between 4 and 5.

1. How do you know it's irrational?

2. How do you know it's between 4 and 5?

Answer 1

1.) you know that 19 is irrational because it is not divisible by any number except 1 and 19 (itself)
2.) you know it’s between 4 and 5 because 4x4=16 and 5x5=25. The square root of 16 is 4 and the square root of 25 is 5. 19 is between 16 and 25; therefore it has to be between 4 and 5.