Question

Between what two consecutive integers do `sqrt50` lie?

Answer 1

`sqrt50` is between `7` and `8`.

Explanation:

We can list out some of the squares and square roots that we know (I'll start from `5`):

`color(white){color(black)( (qquadqquad 5, qquadqquad sqrt25), (qquadqquad 6, qquadqquad sqrt36), (qquadqquad 7, qquadqquad sqrt49), (qquadqquad 8, qquadqquad sqrt64), (qquadqquad 9, qquadqquad sqrt81):}`

We can see that `sqrt50` would lie in between `sqrt49` and `sqrt64`, so that means that `sqrt50` is between `7` and `8`.

Using a calculator, we can validate this:

`sqrt50~~7.0710678...`