Square root interview question

Imagine some of the answers you might get to  “What is the square root of 101?” First, three answers that suggest an interviewee is not strong with math.

  • What’s a square root?
  • You gotta calculator?
  • 101 doesn’t have a square root.

And here are some other answers that might give an idea where an interviewee is coming from.

  • An irrational number. (Pure mathematician)
  • Approximately 10. (Engineer)
  • Somewhere between 10 and 11, closer to 10. (Better engineer)
  • Approximately 10.05, based on a linear Taylor approximation centered at 100 (Applied mathematician)
  • Approximately 10.05, based on one step of Newton’s method (Computer scientist)

(This is just for amusement. I don’t think quiz show-like interviews are a good way to find people you want to work with for years.)

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53 thoughts on “Square root interview question

  1. How about: The square root of 101 is a number which, when squared, equals 101.

    Although I agree that the question can discriminate, in a very coarse way, the mathematical level of the interviewee, I am not sure if I would ever ask such a question.
    The reason being that if it is relevant to know a “good” answer to the question then there are better questions i.e. questions that better reveal the mathematical level of the interviewee.
    But if it is not relevant to know a “good” answer why ask the question?

    So could you explain when you would ask such a question?

  2. Well, my instinctive response was the linear approximation, which means that I’m making progress in my quest towards usefulness, given my roots in pure mathematics.

    Newton’s method never entered my mind. It always felt like an afterthought in Calc I . . . the type of section that prevents you from covering all that you really wanted to accomplish.

  3. Eric: Newton’s method is actually how some chips calculate square roots.

    Daan: Your comment may have come in before I updated the post with the disclaimer that I wouldn’t actually use this in an interview.

    When would I ask such a question? In teaching, not in an interview. This post was inspired by a conversation I had with one of my children. She was computing square roots using a calculator with no square root key, basically using the bisection algorithm, though she doesn’t know it’s called that.

    I thought about how many of her peers would probably say “101 doesn’t have a square root.” Simple homework assignments implicitly teach kids that anything that doesn’t have a simple answer doesn’t have an answer. If you explicitly say an answer can be any real number but you implicitly say that it must be an integer (via examples), most kids will think integers.

  4. Perhaps the interviewer’s question “What is the square root of 101?” indicates his own mathematical weakness, as there are in fact two square roots of 101.

  5. The following might reveal a pedantic streak in me, but
    √ 101 has one value even though x2 = 101 has two solutions. By definition, √ y means the non-negative solution to the equation x2 = y (assuming y is a non-negative real number).

  6. * order 1 (physicist)
    * order 10 (better physicist)
    * 10 + epsilon (theoretical physicist)

  7. The correct answer is, of course, “I don’t know”. The Windows Calculator suggests the answer might be 10.04987562112089027021926491276 which may or may not be a useful approximation to the unknown.

  8. Muhammad Hussain

    very nice John. First I like the quest for more beyond answer, U r very lucky that you have this quest in the form of your kid. I always appreciate the kids in mathematics, as a programmer I doesn’t like someone uses technology(calculator both scientific and non) in computing their math in lower classes.

    Would it be asked in interviews for a programmer?

  9. Francois Rautenbach

    The question is completely ambiguous. My first question would be if the number (101) is in binary, decimal, hexadecimal, etc.? Second question would be to what accuracy do you want the answer?

    Newton’s method (successive approximation) works fastest overall, but there are other more predictable (time wise) methods.

    BTW, it is quite easy to calculate square roots in your head to at least 5 digits ;-)

  10. Sadly I’d have to admit that the only answer I could give would be that the square root of minus 1 was worked out by Marvin the Paranoid Android (The techie journalist answer)!

  11. Michael Kingsford Gray

    My answer would be a question:
    “In what Domain?”

    When they cannot answer intelligently, I demand that I be interviewed by someone who is better qualified.

  12. OK, got the joke and it was amusing. (The correct answer is 10, you made a small error in formulating the question.)
    The part that really impressed me was:
    …people you want to work with for years.
    I have some (mostly traumatic) experiences with interviews and now I know what I missed in all these situations: humanity.

  13. Frédéric Grosshans

    There was a typo in my previous submitted comment. Here is the corrected version. Sorry.

    Approximately 10.05 based on one step of Babylonian method: Someone with an interest in the history of calculation. Unless you think Babylonians writing on cuneiform tablets a few millenia ago were computer scientists using Newton’s methods ;-)

  14. Christian Sciberras

    What do you mean by “pure mathematician”? Someone that excels in mathematics, or one that is familiar with “pure mathematics”?

    I’m asking because I would have replied “an irrational number”, since (to an extent), I’ve studied pure mathematics, but mathematics really isn’t my strong point (quite the contrary, arguably).

  15. Isn’t 101 (bin) = 5 (dec)…
    Surely the question should be “what’s the square root of 1001”, for the answer “11” ;-)

  16. As a software engineer, I suggest that the question is valid in an interview, not to see if the person understands mathematics, but to see how the person would approach the problem. As indicated by the many responses to the original post by John, there could be many solutions (some better/more accurate than others). How the interviewee would get the answer says something about their problem solving skills.

    Nice thought provocation, John :) Tell your daughter ‘Thanks’ for all of us.

  17. I think this can sometimes be a useful interview question. We sometimes use a square root question, or a question like “How many basketballs can I fit in this room?” when interviewing entry-level programmers. Some will respond by staring blankly out the window and throwing out a number. When we then ask how they came up with the number they say, “I just guessed.”. Others will breakdown the question in their mind, perhaps measure the width, height, and length of the room with their eyes, then provide a close approximation to the actual answer. If all else in the interview were equal, it is an individual from this latter group that I would prefer to hire.

  18. I once faced exactly this question.

    At the time, only final year students were allowed access to the University’s computer (yes, singular, very long time ago) and as a first year I had to obtain special permission from the dean.

    My answer was: “I can’t do square roots in my head , and that’s precisely why I need to learn how to program computers.” Don’t know whether he liked the answer, but I got the permission.

  19. I thought about how many of her peers would probably say “101 doesn’t have a square root.” Simple homework assignments implicitly teach kids that anything that doesn’t have a simple answer doesn’t have an answer.

    Yes, I remember some of teachers in the primary school who just said – it is impossible to find a square root of such a number or You can find a non integer power of number.

    I think that if kid has such a question – it would be better to show that new way of finding root or power, because he is really interested in and probably he will be much more.

  20. So what if the interviewee answered SQRT(100) + SQRT(1), which is equal to 10 plus an irrational number?

  21. I’m no mathematician.
    I knew that 10^2 is 100 and 11^2 is 121.
    So that led me to believe that the answer was around 10 plus 1/21. 1/20 is .05.
    So I would have answered “Approximately 10.049 but I’m not smart enough to get any closer”.
    Just interpolation.
    If that decided them to go with someone else , then clearly the job required someone else.

  22. “That’s like asking the square root of a million. No one will ever know.”
    ~ Nelson Muntz, The Simpsons

    Thanks for the chuckle.

    I did Euler – also gives 10.05 at round one. At round two, I couldn’t do 1/8040 in my head having to settle for 10.049875 derived from 1/8000. Since I had to cheat the round two answer, I knew better than to attempt round three without mechanical assistance, e.g., paper, pencil, calculator, etc., and quit. I liked the linear differential approximations, since this is the square-root function, decreasingly increasing, and we’re in the neighborhood of 100 – the tangents are pretty close to the function especially for small delta-x.

    My problem is that I’m now confused about whether I’m still an applied mathematician or a computer programmer or either, since I picked neither Taylor nor Newton and considered the behavior of the subject function over the interval of interest in electing a method of approximation.

  23. hey, no body mentions that the square root is a geometrical concept to begging with. The fact that we can not represented it in a digital (discrete-information) way is anecdotal.

  24. You forgot an answer like this:

    We can understimate it as 10, and do our computation with this exact value in order to obtain just the order of magnitude of the result (lazy physicist)

  25. IBM Scientists Pre-Watson: 10 + 1 * fractal dimension( 101), since 101 is a partial fractal consisting of a 10 by 10 square and a 1 by 1 square…
    IBM Watson: What is ..%$^^! [ERROR] InvalidVendorException Stack Trace:

  26. Java Architect (pre-agile era) There is an open source framework based on BouncingCat that fully implements Intelligence Injection Pattern that will compute square roots for all odd numbers.

    Java Architect: We will go with 10 in the first scrum iteration and then we will wait for requirements clarifications from the business analysts.

  27. Linux Developer: I am not sure bout the squally root, but the half-root of 101 is 1c. I swear on my beard that I never heard that palindrome numbers have HEX roots. Groovy!

    A beginner Perl programmer: Don’t feed the trolls!

    Your bosses school buddy during an interview for the CTO position: “101”, yeah sure I know that! All my courses were about 101.

  28. A correct answer in the state of Indiana: By the state law the square root of 101 is 16/5 and Pi is 22/7’.

    a. Printing typo: the legally correct value of square root of 101 is not 16/5, but 113/11.
    b. Due to meddling of a mathematician into the legal matters “The Pi Bill” never become a low. It is still pending decision of Indiana Senate. If you are reside in the state of Indiana, please contact your state representative and ask him/her to finally pass this fine bill. Internets are waiting.

  30. BlueCollarCritic

    I guess I’m one of the non-mathmaticians since I quickly guessed, as one would probably have to do when asked this on the spot during an intevriew, the answer was ‘10.1’ . Before reading the asnwer I thought about it some (something you wouldn;t do in an interview) and realized it was too high but for an aproximation I thought it was fairly close considering the on the spot scenario it was asked.

    BTW – If one were trying to surmise the canidataes analytical skills, wouldn’t a better version of this be …

    What is the square root of 1?

    The simplicty of the calculations to derive this answer make it somewhat of a trick question without really being one. It can help determine if one tries to over think something; but thats just an opinion. I for one never want to go back to having to interview people as I am a probelm solver and not a manager of people.

  31. Michael Kingsford Gray

    “What is the square root of 1?”

    1 & -1, for starters.
    The question implies the singular, and is therefore poorly couched.
    I’d sack the interviewer if they asked this nonsense question.
    If they asked:
    “What are the square roots of 1?”, I’d be happier.

  32. BlueCollarCritic

    @Michael Kingsford Gray

    Its called a trick question. It wasn’t intended to be on the level of providing a proof for Riemann’s hypothesis.

    You’d sack the interviewer ey? Are you currently employed? If not I’d recomend you not think about that kind of action unless you want to be unemployed.

  33. Michael Kingsford Gray

    I am now, and have always been self-employed.
    I do not need to impress an interviewer for my income.
    I employ others.

    I never use “trick questions” when interviewing potential staff.
    I maintain that if any interviewer in my employ implemented that trivially useless question, trick or not, I would seriously consider giving them the sack.

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