Harvard University Admission Interview Tricks | 99% Failed Admission Exam | Algebra Aptitude Test

[@caperider1160]

Nice algebraic trick. But i doubt if this was actually a Harvard entrance exam question.

[@AsadInternationalAcademy]

thank you so much!

[@AsadInternationalAcademy]

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[@AsadInternationalAcademy]

math olympiad question

[@caperider1160]

@@AsadInternationalAcademy that's more like it. Its lots of puzzle with little maths

[@mtreding]

Harvard doesn’t have an ‘entrance exam’ 😂

[@davidreid7293]

Or sqrt of 49 = 7 and sqrt of 4489 = 67 and sqrt of 444889 = 667 and sqrt of 44448889 = 6667 so sqrt of 4444488889 = 66667.

[@AsadInternationalAcademy]

nice job

[@AsadInternationalAcademy]

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[@kunalkashelani585]

Such a beautiful solution!

[@AsadInternationalAcademy]

Glad you think so!

[@AsadInternationalAcademy]

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[@dolhijn]

I dont get the step where you omit the 12b

[@alanjones4358]

The Babylonian method is easier and quicker. Nice video just to illustrate a different way to solve.

[@AsadInternationalAcademy]

Cool, thanks

[@AsadInternationalAcademy]

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[@smokeldogg]

Easy, answer is X.

[@AsadInternationalAcademy]

Yes, it's easy

[@AsadInternationalAcademy]

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[@TomKaren94]

I just did it the basic long way. Took a minute but i got there

[@AsadInternationalAcademy]

Wonderful job, thanks

[@AsadInternationalAcademy]

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[@AmitKumar-er6fz]

How do you in starting that it is a perfect Square

[@AsadInternationalAcademy]

The square root of 4444488889 is 66667. It is a perfect power (a square), and thus also a powerful number. 4444488889 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

[@AsadInternationalAcademy]

It can be written as a sum of positive squares in only one way, i.e., 4061895289 + 382593600 = 63733^2 + 19560^2 . It is not a de Polignac number, because 4444488889 - 211 = 4444486841 is a prime. It is a Duffinian number. It is a plaindrome in base 10. It is not an unprimeable number, because it can be changed into a prime (4444488883) by changing a digit. It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 10866517 + ... + 10866925.

[@AsadInternationalAcademy]

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[@venkatk1968]

Nice. But how would one know that this is the way to solve it?

[@AsadInternationalAcademy]

Thanks, there are more methods to solve this, not only this. But, I'm sure, this is the easiest method than others

[@AsadInternationalAcademy]

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[@JustBadMeAndI]

I would take my phone (calculator)out of my pocket. 😮

[@AsadInternationalAcademy]

ok

[@AsadInternationalAcademy]

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[@nenemtiaof5016]

What about 12B ?

[@AsadInternationalAcademy]

very simple, follow the steps

[@AsadInternationalAcademy]

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[@quadibloc2]

64 is 8 squared, and 63 is 7 times 9. In general, n^2-1 is (n+1)*(n-1). If I subtract 1 from 4444488889, I get 4444488888, and that has obvious factors. It's 100002 times 44444. 100002 has digits that add to 3, divide by 3, get 33334. So the number minus one is equal to 33334 times 3 times 11111 times 4. 33334 and 33333 differ by 1; we want numbers that differ by 2, so take one of the twos out of 4. The answer seems to be 66667*sqrt(2).

[@AsadInternationalAcademy]

okay thanks

[@AsadInternationalAcademy]

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[@tassiedevil2200]

@quadibloc2 - you seem to have picked up a spurious factor of sqrt(2)?

[@BossDropbear]

Calculator on your phone says 66667.

[@xaviconde]

I was tought in school how to calculate square roots by hand, don't know how difficult would be to get this solution.

[@AsadInternationalAcademy]

this is easy problem

[@AsadInternationalAcademy]

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[@HartmutRick]

I tried, it took me about 3 minutes.

[@terencetwentyman-jones8861]

Please write slower, I cant follow that fast....

[@AsadInternationalAcademy]

no problem, you can slow the speed, see options

[@AsadInternationalAcademy]

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[@ralphmelvin1046]

Do it by number my number right going left

[@AsadInternationalAcademy]

okay but this method is very simple and easy to understand

[@AsadInternationalAcademy]

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[@AtıfAkça]

❤

[@AsadInternationalAcademy]

thank you so much!

[@AsadInternationalAcademy]

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[@AsadInternationalAcademy]

you should share this lesson

[@dexcortez7425]

AcademicaLy pretty Not practicaL to daiLy Life

[@AsadInternationalAcademy]

thanks

[@AsadInternationalAcademy]

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[@andrewmiles187]

Well the actual answer is 66667 or -66667 so where is the working for that

[@AsadInternationalAcademy]

Good job! thanks

[@AsadInternationalAcademy]

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[@rainerzufall42]

Not a good job, because that's plain wrong! For starters: sqrt(y) = x => only one solution (with x >= 0 for non-negative real y), it's called the principal square root. y = x² => two solutions, + sqrt(y) and - sqrt(y). Still sqrt(y) is only the positive root here, the sign is on the outer side!

[@rainerzufall42]

For the latter: if y = 0, there's only one solution, and that's x = 0. For y < 0, there's no real solution. But that's just a disclaimer!

[@andrewmiles187]

@rainerzufall42 where does it say that it has to be positive only, the squareroot of 4 is 2 or -2, same here but 66667 and -66667

[@sumdumbmick]

try v(2004848)

[@AsadInternationalAcademy]

nice idea, thanks

[@AsadInternationalAcademy]

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