Question

Without using a calculator, fill in the blanks with two consecutive integers to complete the in equality

Answer 1

`4 < √(17) < 5`

Explanation:

Mumble. The square root is something called "monotonic", which means that
`a > b \Leftrightarrow \sqrt a > \sqrt b`

A neat trick to solve this will be: go back from 17 till you find a perfect square, then add 1 to it:

In our case it's easy to do it, since the number before 17 is a perfect square already (
`16=4^2`), so we can pick it as the lower bound, and then add 1 to the base to find the next one (
`4+1= 5)`

Answer 2

`√(16) < √(17) < √(18)`

Explanation: