The Square Root of 98

By JoAnne Hewett | September 20, 2006 11:26 pm

I bet you all are not aware, but there is a new test of nationality being performed when one enters the US. I arrived in the San Francisco airport on Monday night, passed passport control, picked up my luggage, and went to hand in my customs form, which is the last step in the arrivals process. The customs agent stopped me dead in my tracks. He first asked, “Are you an American.” Obviously I answered “yes” straight-away. Then he asked, “OK, then, what is the square root of 98?”

Now, this is a question that me of all people (given what I do for a living) can answer, instantaneously. But, at the time all I could do was turn towards the guy and utter “HUH?” There were three things on my mind:

  • I had already passed passport control. This guy was a CUSTOMS agent. Why was he checking my nationality?
  • I had been traveling for 23 hours. I left my hotel room in Venice at 5:10 AM, took a boat to the train station, took a train to the mainland, took a train back to Trieste (I won’t mention the trauma associated with catching that train or knowing that it was the correct train…), took a bus from the train station to the airport in Trieste (I won’t mention the trauma wondering if the bus was going to make it on time to the airport so I could catch my flight), took a flight to Munich, sat in the Munich airport for 4 hours, then finally took the 11 hour flight back home to California….I understandably was a bit dazed after all that!
  • I was smuggling suspicious cheese in my backpack. The last thing I needed was a customs agent with funny questions! I was in Europe, meaning I went to a cheese shop, selected some cheese, and they carved out some hunks from the large rounds of cheese and wrapped it in wax paper. There is no packaging and no information on the pasteurization process…
  • So, after I gave my intelligent answer of “HUH,” the guy burst out laughing and said, “Yes, of course you’re an American. You don’t know anything!”

    I wonder what would have happened if I had been awake. My normal, instantaneous response would have been “7 times the square root of 2”. I wonder if I would have been arrested if I said that….

    • Sean

      What do you mean, you couldn’t you take the square root of 98 instantly? Is it because you’re a woman?

    • JoAnne

      Even worse, I’m an American woman!

    • jay

      But still you are not a string theorist who usually disregards factors like 2 or pi, or whatnot, are you?

    • Louise

      9.9 and welcome to the US! Since you are in the San Jose area, you should check out the AIAA Meeting ending Thursday. The 50th anniversay of the Particle Data Group is being celebrated at LBL Saturday. (AIAA has better blog pictures)

    • Anonymous

      After several seconds of thought, I came out with 7*1.414=9.898. (Actual answer is 9.98949 … it never occured to me to quote the result as a square root.) Am I going to jail?

    • Sam Gralla

      cute. I might have said, “it’s as irrational as your question” ;p

      (I would never have thought of that, but fun to fantasize)

    • oenamen

      Isn’t the normal physicists response that the square root of 98 is 10? 😉

    • Rob Knop

      I would’ve said “a wee bit less than ten”. Perhaps using “wee” would have made him think I was Scottish. I dunno.

      Bizarre question. I’m guessing the Customs agent was also at the end of a very long shift….

    • schnitzi

      >Actual answer is 9.98949

      You can always tell a *quantum* physicists — they’re the ones that say “plus or minus” in front of their answers…

    • Stuart P

      Pardon my ignorance, but how did you instantly arrive at 7 times the square root of two?

    • Count Iblis

      No, the approximate answer is 9.89950 pm 10^{-5} which you can find by doing a Taylor expansion about 100 (you only need the first two terms and). You can do this in your head, because the Taylor expansion about 100 yields almost immediately the decimal expansion.

      Some time ago I read that many algorithms used for elementary computations and sysmbolic computations actually derive from an algorithm to compute 1/X without doing any divisions. This works by applying Newton’s method to the equation

      Y – 1/X = 0

      For the (n+1)-th approximation you get:

      X_(n+1) = 2 X_(n) – Y X_(n)^2

      This is convenient because there are no divisions in here. Also, you double the number of significant digits after every iteration instead of getting only one new digit as in long division.

      But the real nice thing about this is that you can compute almost everything using this algorithm. If Y is a power series instead of a number, then the algorithm will converge to the power series of 1/Y, doubling the number of correct terms in each iteration.

      If you can compute 1/Y, you can compute
      Log[Y] by integrating term by term Y’/Y.

      Using the algorithm for the logarithm you can compute Exp[Y] by solving the equation Y – Log[X] = 0 using Newton’s method, which again doesn’t contain any divisions.

      By combining these algorithms you can compute the first n terms of any power series in a few times log(n) steps.

    • Count Iblis

      I forgot to mention that multiplying to large powerseries with n terms takes sim log(n) steps if you use fast Fourier transformation.

    • Ambitwistor


      If you know that 98 = 49 * 2, which is not hard to figure out even if you don’t know it (since 100 = 50 * 2), then sqrt(98) = sqrt(49) * sqrt(2), or 7 * sqrt(2).

    • Goldenship2

      So, what is a square root?
      How many sides does a square root have?
      Can you drink square root beer?
      And does that entitle aliens to a green card

    • Constance Reader

      I thought the only thing with a square root was a box plant…

    • little

      What a strange question is!
      I am curious about all kinds of questions the custom agent has in mind.

    • Sean

      I know what to ask to tell whether people are French.

    • B

      Hi JoAnne,

      Thanks for this hilarious post :-) Google knows everything. Best,


    • Rob Knop

      Sean — I don’t have Flash running on my computer, so I didn’t see the video, but let me guess:

      The Sun, the Moon, and indeed the Earth all orbit around France.

      Yes? :)

      -Rob (who knows that the true center of human culture and indeed the barycenter of the Universe is the deep southeast of the USA, and you can have that barycenter when you pry it from his cold, dead hands)

    • Jeff

      i once had a customs agent (of asian ethnicities) see all my Asian passport stamps, including Korea, ask me “So…did you like Korea and the Koreans? I hate ’em….” Is that a loaded trap question or just plain illegal? I said I had a perfectly fine time and he shrugged but let me through…

    • Tony Smith

      JoAnne, you said that you “… left … Venice …[and]… took a train back to Trieste ….” and then flew (through Munich) to California.
      My guess is that the train leg of your travel led to some suspicion, and that it has been (since even before 911) a practice to check closely those with a profile of a European train trip leading to an air flight to the USA (effectively a one-way air ticket).
      Many years ago (well before 911) I took a train from Hamburg to Goteborg and then a FinnAir flight to Amsterdam connecting with a Delta flight to Atlanta. At the Amsterdam airport, the gate person said (in Dutch) “He fits the profile”, whereupon I was invited to go into the secure concrete bunker in the airport basement, surrounded by heavily armed military guys. They had my luggage, and asked if I had “anything that could be used as a weapon”, and I said “Of course, yes”, and they said “show it to us”, and I showed them a Swiss army knife, and they all burst out in laughter and said “get on the plane”.
      I have no idea what I would have said had they asked me for the “square root of 98”, but it is indeed sad that ignorance is now a way to prove USA citizenship, and that an answer other than “HUH” might have gotten you a free vacation in Castro-free Cuba.

      Tony Smith

    • Carl Brannen

      I would think that the combination of an Iowa and California accent would have been more than sufficient.

    • Stuart P

      Thanks, Ambitwistor.

    • PK

      Rob, it’s even better: he asks the audience…

    • rob ezerman

      “Security” of all stripes are taught to ask an uncomfortable or impossible question as a general screening test: to be uncomfortable the question, at a gut level should relate to the “subject” and be difficult to answer. Sweat then = guilt of some sort. Rob

    • B

      Some years ago, I accidentally crossed the border to Mexico without having all my visa documents with me. It’s fairly easy to LEAVE the US without even noticing it, but on the way back I ran into a problem with the border post in Nogales. I told them I work at the Department of Physics at the University of Arizona, and they demanded I proof that I am a physicist. I asked them, well what do you want? Equations on a notepad? A lecture about Supersymmetry? Eventually I told them to look up my webpage with the publication list, which kind of convinced them that I wasn’t trying to smuggle black hole bombs or the like.

      What I realized though (besides to always take my passport with me) is that it helps to use words everybody obviously connects with physics. Tell them you work on AdS/CFT and they’ll think you’re an insurance agent.

      Best, B.

    • squareroot

      Why 98 of all numbers?
      Is it because 9=3^2 and 8=2^3…maybe the guy is all about super super symmetry:)! And he got the right person to assess that with it…Since I can claim 2 3 8 and 9 in my birthday in a similar fashion, I think I am the living example of supersymmetry. But again it takes a litfetime to explore oneself so when I get a sense of supersymmetry ill pass it along…

    • Aaron

      LOL… thanks for the heads-up!

      the approximate answer is 9.89950 pm 10^{-5}

      Don’t be silly! The square root of 98 is 10… which just so happens to be equal to 3 pi. What a fantastic coincidence! :)

    • Quasar9

      Hi JoAnne,
      as a self-confessed smuggler,
      you are entitled to one night aboard.
      It really doesn’t matter whether the cheese
      has been measured in imperial or metric weight.

      We measure the cheese by its taste
      As long as the cheese tastes real good
      welcome on board you are here understood.
      But I’m guessing there’s little or no cheese left
      so what have you got to offer this hungry pirate instead.

    • Count Iblis

      Aaron, pi^(2) is even closer to the correct answer! B.t.w., orthopositronium lives so long compared to parapositronium, not only because it can only decay into three photons (this makes the decay rate a factor alpha=1/137 slower), but also because the result of the evaluation of the Feynman diagrams contains a factor (pi^2 – 9).

      A more spectacular example of such numerical accidents is the function Exp(Pi*Sqrt(n)) for some integer n, see here.

    • donna

      We just got back from Canada, clearing customs before we got on the ferry. We *still* got questioned by customs agents on the American side, even though we went through American customs in Canada. Stupid stuff, like “why were you in Canada”? when we were crossing over from Vancouver Island, one of the main tourist destinations.

      I wonder why some of these people still have jobs.

    • Quasar9

      ok, after some rivetting pillow talk
      I now know what a square root is.
      I guess one of the multiverse answers is:
      seven x square root of 2

      Well that was more fun than a root canal
      For the first thousand digits of square root of 2
      see rossi sqr2

    • Say Lee

      Some years ago I made a spontaneous but foolish response during my very first arrival at the Heathrow. I raisd my two arms when posed with the seemingly innocuous question from the Customs Lady: Do you carry any arms?

      Even today I still shudder at what could have happened …

      So the Custom Officer of the “Square root of 98” fame could have been dead serious.

    • Peter Erwin


      As to why the Customs agent asked for your passport… there are differences in what you’re allowed to bring in with you, and what you have to pay duty on, depending on whether you’re a US citizen (or permanent resident) or not. (For example, US citizens/residents can bring up to $800 worth of goods duty-free; visitors can bring up to $100 worth of goods they plan to sell or otherwise leave in the US duty-free.)

    • Peter Erwin

      donna said (#31):
      We just got back from Canada, clearing customs before we got on the ferry. We *still* got questioned by customs agents on the American side, even though we went through American customs in Canada. Stupid stuff, like “why were you in Canada”? when we were crossing over from Vancouver Island, one of the main tourist destinations.

      Umm… I’m sure most of the people entering from Vancouver Island are tourists, but there are probably the occasional business travelers.

      As for why they’re asking people seemingly stupid questions at customs… you might take a look at security guru Bruce Schneier’s essay on the subject:

      ON DEC. 14, 1999, Ahmed Ressam tried to enter the United States from Canada at Port Angeles, Wash. He had a suitcase bomb in the trunk of his car. A US customs agent, Diana Dean, questioned him at the border. He was fidgeting, sweaty, and jittery. He avoided eye contact. In Dean’s own words, he was acting “hinky.” Ressam’s car was eventually searched, and he was arrested.

      It wasn’t any one thing that tipped Dean off; it was everything encompassed in the slang term “hinky.” But it worked. The reason there wasn’t a bombing at Los Angeles International Airport around Christmas 1999 was because a trained, knowledgeable security person was paying attention.

    • Quasar9

      And after the all consuming pillow talk
      while I let myself sink into blissful sleep
      I got NASA to compute the
      first 5 million digits of square root of 2
      And I awoke in the morning hungry for more!

    • Amara

      Tony #21: “My guess is that the train leg of your travel led to some suspicion, and that it has been (since even before 911) a practice to check closely those with a profile of a European train trip leading to an air flight to the USA (effectively a one-way air ticket).”


      I think your guess would be wrong. Train travel leading to an airport flight is the most common method of travel with which Europeans reach their airports. In my 8.5 years of living in Europe and ~100 flights (including a couple dozen to the States), I can only count two or three times that I did not have a train trip before.

    • Amara

      Dear JoAnne: If I were to guess about your cheese you were carrying back, it was Parmesian Reggiano, which is not pasteurized. The customs people would know that. However, I wonder about the dogs which are supposed to sniff drugs – what happens if the dogs are hungry and they smell a yummy Parmesan cheese?

      True Parmesian is aged two years, so there is no need for pasteurization (Aging of cheese is equal to pasteurization). Here is something I googled which talks about why and some of the other cheeses that are in the same no-need-to-pasteurize category.

      I suppose your trauma with getting through the trains and to the airport were about lack of signs and other indicators for schedules, tracks and connections plus few Italians understanding English. FWIW, indicators to help travellors do function an order of magnitude better in northern Italy (Trieste, Venice..) than in southern Italy (Rome and south). There is a gradient from north to south. I even have the experience of northern Italians who have visited me near Rome being surprised at the poor functioning of the basic services. I know that doesn’t help you in the trauma you experienced (I’m truly sorry about that), but I’m saying it could have been much worse.

    • Count Iblis

      I’m sure it wasn’t this type of cheese :)

    • Quasar9

      Amara, you fly some dozen times a year? tut tut
      I sincerely hope you’ve planted a veritable forest of trees to compensate for all those air miles, but if you are too busy counting stars, let me know and I’ll be more than happy to plant a few xtra on your behalf
      PS I see at least you let the train take the strain on your way to the airport, but an awful lot of people even in europe still go by private car or taxi.

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    • JoAnne

      Count Iblis: Touché. I didn’t think it was possible, but you have come up with a cheese that I wouldn’t touch with a ten foot pole!

      Amara: I had 3 kinds – a particularly nice strain of Gorgonzola, a peppercorn Pecorino, and a soft sheep’s milk cheese (don’t know the name).

      Tony: While the train theory is interesting, there is no way the customs agent knew I had been on a train.

    • George

      I asked by son, 8, this question. I like is answer the best. Almost 10.

    • citrine

      My mother edited a scientific research journal and used to attend international conferences quite a bit. A customs officer who saw the papers she had with her commented “studying too much is not good for the brain”.

    • Peter

      What I find worse at San Francisco airport, are these ridiculous people trying to get you to donate money. They are standing at a table, calling you over to them, as if they are some official airport people, that you have to go to, to show your passport or something, and then they want you to donate money.

      A lot of foreigners (especially asians) end up donating a lot of money, cuz they don’t know what is going on there.

      I hate the fact that SFO allows this, and I can’t wait for the next time I am going there, so I can mess with these idiots.


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