Between what two consecutive integers do $\sqrt{310}$ $sqrt310$ lie?

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Between what two consecutive integers do $\sqrt{310}$ $sqrt310$ lie?

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Answer 1 · 2015-10-14T13:27:45

Between $17$ $17$ and $18$ $18$ .

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 $10^{2} = 100$ $10^2=100$ , and $20^{2} = 400$ $20^2=400$ . So, $\sqrt{310}$ $sqrt(310)$ will surely be between $10$ $10$ and $20$ $20$ .

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

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

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

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

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Between what two consecutive integers do $\sqrt{310}$ $sqrt310$ lie?

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Between what two consecutive integers do $\sqrt{310}$ $sqrt310$ lie?