# Between what two consecutive integers do sqrt310 lie?

Oct 14, 2015

Between $17$ and $18$.

#### Explanation:

I'd say that the simpliest way is just to go and try, of course with a little bit of wisdom.
For example, we know (or easily compute) that ${10}^{2} = 100$, and ${20}^{2} = 400$. So, $\sqrt{310}$ will surely be between $10$ and $20$.

Now we narrow our search by confronting with midpoints: ${15}^{2} = 225$, so $\sqrt{310}$ is between $15$ and $20$.

Since ${17}^{2} = 289$, $\sqrt{310}$ must be between $17$ and $20$

But ${18}^{2} = 324$, so $\sqrt{310}$ is exactly between $17$ and $18$.

Of course, I solved the exercise using only confrontations and easy computing. One immediate way is simply to ask any calculator for $\sqrt{310}$, he will give you back $17.6068 \ldots$ and you'll immediately get the solution.