Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $x,y$ $\in\mathbb{R}$ and $\lfloor x\rfloor = 10$ and $\lfloor y\rfloor = 14$.

Need to compute: $\sqrt{\lfloor\sqrt{\left|x+y\right|}\rfloor}= \; ?$


$$10\le x < 11$$

$$14\le y < 15$$

So $$24\le x+y < 26.$$

But then i don't know what to say about:

$$\lfloor\sqrt{|x+y|}\rfloor = \ldots$$

Because i don't get what is the use here for the absolute part: what his role here?

And how can i proceed?


share|cite|improve this question
The absolute value is a no-op there, you can ignore it. Under the constraints, what can $\lfloor \sqrt{x+y}\rfloor$ be? – Daniel Fischer Feb 25 '14 at 22:54
i think that $4$? – feder Feb 25 '14 at 22:56
Well, that or ...? – Daniel Fischer Feb 25 '14 at 22:56
@feder Couldn't it be $5$ as well? – AnonSubmitter85 Feb 25 '14 at 22:57
that or $5$? not sure how to show that, just by intuition – feder Feb 25 '14 at 22:57

2 Answers 2

up vote 2 down vote accepted

What you did so far is good. Now justify these steps: \begin{align*} 24 &\le x + y < 26 \\ 24 &\le |x + y| < 26 \\ \sqrt{24} &\le \sqrt{|x + y|} < \sqrt{26} \\ 4 &\le \left\lfloor{\sqrt{|x + y|}} \right\rfloor \le 5 \\ \sqrt{\left\lfloor{\sqrt{|x + y|}} \right\rfloor} &= 2 \text{ or } \sqrt{5} \end{align*} Indeed, as Ross Millikan states, there are two possible answers. If you expected a single answer, you must not have written the question exactly right.

share|cite|improve this answer
i expected two answers so thanks alot!:) – feder Feb 25 '14 at 23:39

Since you know $x+y > 0$, you know $|x+y|=x+y$ and you can remove the absolute value bars. They were just there to confuse you. You won't get a single answer.

share|cite|improve this answer
so i can tell by the two inequalities that the values of $\lfloor \sqrt{x+y}\rfloor$ could be $4$ or $5$ so the answer would be $2$ or $\sqrt5$? but how can i show algebraic the the values can be $4$ or $5$? – feder Feb 25 '14 at 23:01
Post this as a comment to his question, please. – Brian J. Fink Feb 25 '14 at 23:03
@BrianJ.Fink Why? It is common to answer questions with a hint rather than a full solution when that is deemed appropriate. – 6005 Feb 25 '14 at 23:07
Sorry I misunderstood the words "not...a single answer." – Brian J. Fink Feb 25 '14 at 23:10
@BrianJ.Fink I've made a trivial edit you should be able to remove the dv – TooTone Feb 25 '14 at 23:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.