# Between what two consecutive integers do sqrt50 lie?

Mar 13, 2018

$\sqrt{50}$ 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 $\sqrt{50}$ would lie in between $\sqrt{49}$ and $\sqrt{64}$, so that means that $\sqrt{50}$ is between $7$ and $8$.

Using a calculator, we can validate this:

$\sqrt{50} \approx 7.0710678 \ldots$