Much quicker and easier to just treat 5^11 as 5^4 x 5^4 x 5^3, which is 625 x 625 x 125. Multiply 625 x 625 and then multiply that product by 125. Then subtract 9. This is much faster than the method shown.
After puzzling over this, the simplest solution seemed to me to be E = ((5^5)^2)*5 - 9; 5^5=3,125; so by long multiplication 3,125*3,125 = 9,765,625 then 9,765,625 * 5 = 48,828,125, and finally 48,828,125 - 9 = 48,828,116; or written out using segmentation and group multiplication, 3,125 * 3,125 = 3,000 * 3,125 + 100 * 3,125 + 20 *3,125 + 5 * 3,125 =9,765,625
As others have said, there are several fairly direct calculations of 5^11 that are probably easier. I choose to use 5^11 = 5 * (5^5)^2 = 10 * (3125*3125)/2. The only non trivial steps in this calculation are a single 4 digit x 4 digit long multiplication and a divide by 2.
10**11/2**11 would really be faster to obtain using long division. also during the solution it would be useful to remember that 24+26=50 and 24*26=(25-1)*(25+1)=25**2-1
Using a similar-ish method we can tackle this puzzle: what is 2^5 ? [NO CALCULATORS ALLOWED] 2^5 = (10-8)^5 = 10^5 - 5*10^4*8 + 10*10^3*8^2 - 10*10^2*8^3 + 5*10*8^4 - 8^5 = 100000 - 400000 + 640000 - 512000 + 204800 - 8^5 = 32800 - (2^5)^3 Now (and this is the clever part) setting x = 2^5, we get x = 32800 - x^3. Or x^3 + x - 32800 = 0. So we have reduced our original puzzle to a simple cubic equation!
I would just do: 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 48,828,125 3 x 3 = 9 48,828,125 - 9 = 48,828,116 So the answer is 48,828,116. I would of course do this all on paper by hand since no calculators are allowed. There’s no reason whatsoever to make it complicated, it’s as easy as that.
Was the intent to solve the question in the hardest way possible? I can devise a harder solution then yours. How about changing the numbers to base 17 before calculating...
This is one of those contrived special-case problems that gives math instruction a bad name. It isn't even one of those convoluted methods that was developed to do arithmetic in the days before computers -- it's easy enough to multiply out by hand (if anyone remembers how to do that). It's a pointless puzzle problem that has no place in a math curriculum.
So, you did not ask for simplification but for a number. As, in any case you did long multiplication, it would have been faster to do a = 625 * 625 * 125 - 9
@@hamzagezici1731 thank you. 10^3/2^4 is a very useful ratio to avoid long division by 2048. and indeed, 10^11/2^4 = 5^4*10^7 which is then easier to divide by 2^7
This problem becomes much easier if you change base: 5^11 - 3^2 (base 10) = 100000000000 - 14 (base 5) = 44444444431 (base 5) Converting the final answer back to base 10 is left as an exercise for the reader.
Wow. When I saw all the bases and exponents were different prime numbers, I didn't see where to start, though of course was looking for x^2 -- y^2 somewhere. This was great.
Notice that there is a mistake in calculations. After factoring out 5 and applying the rule of two squares equals sum times difference of squared numbers, you forgot to put it in square brackets. As a consequence you only multiply the first addend of the sum. Please correct me if I am wrong.
Stan,this is from sthan Arabic and Sanskrit meaning place country village or town Ford English a place of shallow water wet mud or pond . Stanford meaning a shallow water place where university is built.Thank you.
I guess that professors in mathematics from Stanford University, learned at secondary school already in "calculator era". So, they probably do not know about multiplication in column method.
It’s all about logic and problem-solving, not just calculation methods. 👍This problem tests your understanding of concepts, not your calculator skills 😎💯💕🙏
@@superacademy247 Excuse me, if multiplication in column works here faster, let say, it is not the best example of the problem. Should be common sense anyway. And, by the way, how did you get 5^5 so quickly?
I would like to see some proof that this question, and others like it, were actually posed by reputable bodies. They just don't have the right 'vibe', and look as though they have been invented purely for sites like this one. Academics might well ask, "how would you solve this?". But as soon as one mentioned surds, they would move on to something else and not expect lots of tedious manipulation. Academia ranks insight far above kindergarten arithmetic.
I can't see any reason to calculate like this, just calculate 5 by 5, 5^2=25, 5^4=625, 5^5=3125, 5^10 = (3100+25)^2= 3100^2+2*3100*25+25^2=9610000+155000+625=9765625, then multiply by 5 and minus 9. multi-power of 5 should be an easy calculation, the method here is just nonsense.
Here's what I did: 5¹¹-3²=5³5⁸-3²=5³(5⁸-3²)+5³3²-3²=5³(5⁴+3)(5⁴-3)+5(5²3²)-3²=125(625+3)(625-3)+5(15²)-9 =(1000/8)(628)(622)+5(225)-9=(1000)(628/4)(622/2)+1125-9=(1000)(157)(311)+1116 =(1000)(48827)+1116=48827000+1116=48828116
For most of the commentators: this kind of exercise is for testing the imagination, beligerancy and resiliency of the candidate. So, congratulations, most of you would have passed the test. 😄
I like your solution too. 5^5=5*25^2=5*625=3125 Next, use a trick for squaring numbers that end in 5 5^10=3125^2=(300+12)(300+13)100+25=(90000+7500+156)100+25=9765625 5^11=5*5^10=97656250/2=48828125
in english the letter "b" is pronounced as in "baby" not as in "papa" ... quite distracting also "a*b" is not read as "a into b" - rather "a times b" ... quite distracting
Much quicker and easier to just treat 5^11 as 5^4 x 5^4 x 5^3, which is 625 x 625 x 125. Multiply 625 x 625 and then multiply that product by 125. Then subtract 9. This is much faster than the method shown.
Your last sentence is redundant.
Yes, calculating 5^11 by hand is indeed quite easy
An easier way to handle a number x 125 is to multiply the number by 1000 and then divide the result by 8. E.g. 496 x 125 =496000 ÷ 8 =....
Video is much more "simplified" as per ask
Not a good way to solve the problem
This video is not about solving the equation, it is teaching us how to make a long form video with simple maths problem 😂
I appreciate your perspective! 🤩Thanks for your feedback! 💯😎
@ just kidding ya lol😂
Z😂
Takes less time to just multiply out the numbers.
Thank you! I did it in at most 3 minutes.
Exactly, I was gonna say that, too
lol yes
It's about the algebra, not the fastest route
Riduculous. Making a meal of an extremely simple problem.
Explains why Stanford is down the tubes?
They are woke and ElGeeBeeTeaWue.
@@dalepeters4927
Indeed
After puzzling over this, the simplest solution seemed to me to be E = ((5^5)^2)*5 - 9; 5^5=3,125; so by long multiplication 3,125*3,125 = 9,765,625 then 9,765,625 * 5 = 48,828,125, and finally 48,828,125 - 9 = 48,828,116; or written out using segmentation and group multiplication, 3,125 * 3,125 = 3,000 * 3,125 + 100 * 3,125 + 20 *3,125 + 5 * 3,125 =9,765,625
Wow! ✅
@@superacademy247Agree. This is not useful
Totally agree with everyone else. Much quicker and easier to just multiply the numbers out from the word go.
As others have said, there are several fairly direct calculations of 5^11 that are probably easier.
I choose to use 5^11 = 5 * (5^5)^2 = 10 * (3125*3125)/2.
The only non trivial steps in this calculation are a single 4 digit x 4 digit long multiplication and a divide by 2.
I'm glad you found a simpler way to solve the problem! Thanks for sharing it with everyone. 🚀🙏✅👏
5 x 3125 x 3125 - 9 is just as simple as 5 x 3126 x 3124 - 4, without the unnecessary steps of the first 4 minutes.
Then how can you make such videos and earn money. This is also a strategy that Olympiad ques. are tough .
10**11/2**11 would really be faster to obtain using long division.
also during the solution it would be useful to remember that 24+26=50 and 24*26=(25-1)*(25+1)=25**2-1
I appreciate you watching! 👍💯Thanks for the feedback! 💕🥰✅Thanks for sharing your solution! 💯🙏🔥
There is no one best way to do this problem. But with no calculator, I chose 100,000,000,00 ÷ 2048 - 9
your power of ten has 10 zeros while it should have 11
Instead of long division by 2048, perhaps it simpler to just keep on dividing by 2 (eleven times...)?
@@rclrd1 long division would require fewer steps. but more attention from the human :>
Using a similar-ish method we can tackle this puzzle: what is 2^5 ?
[NO CALCULATORS ALLOWED]
2^5 =
(10-8)^5 =
10^5 - 5*10^4*8 + 10*10^3*8^2 - 10*10^2*8^3 + 5*10*8^4 - 8^5
= 100000 - 400000 + 640000 - 512000 + 204800 - 8^5
= 32800 - (2^5)^3
Now (and this is the clever part) setting x = 2^5, we get x = 32800 - x^3. Or x^3 + x - 32800 = 0. So we have reduced our original puzzle to a simple cubic equation!
I would just do:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 48,828,125
3 x 3 = 9
48,828,125 - 9 = 48,828,116
So the answer is 48,828,116.
I would of course do this all on paper by hand since no calculators are allowed. There’s no reason whatsoever to make it complicated, it’s as easy as that.
5¹¹=5•5•5•5•5•5•5•5•5•5•5 ??? 😳
5¹¹=(10/2)¹¹=10¹¹/2¹¹=
=10¹¹/2/2/2/2/2/2/2/2/2/2/2 😁
Great lesson is the variety of techniques available in solving these types of problems. Thank you!
Taking the algebrauc route is beautiful to see. Thank you
Thanks for appreciating the algebraic approach! 🔥💪
Was the intent to solve the question in the hardest way possible? I can devise a harder solution then yours. How about changing the numbers to base 17 before calculating...
Calculation in base 5 might be optimal 😁 100000000000-14
This is one of those contrived special-case problems that gives math instruction a bad name. It isn't even one of those convoluted methods that was developed to do arithmetic in the days before computers -- it's easy enough to multiply out by hand (if anyone remembers how to do that). It's a pointless puzzle problem that has no place in a math curriculum.
So, you did not ask for simplification but for a number. As, in any case you did long multiplication, it would have been faster to do a = 625 * 625 * 125 - 9
penjelasannya dibuat rumit..padahal sangat mudah, menit 10:48 = 3.16 x 3.124x5 -4 = 48.828.116
If you still have to remember 5^5=3125 and you can only simplify the calculation, then just use a computer to do it.
Stanford University Admission Simplification Problem: 5¹¹ - 3² =?
5¹¹ = (5²)(5³)³ = (25)(5³)(5³)² = (25)(125)(125²)
125² = (10² + 25)² = 10⁴ + 5(10³) + 25² = 10⁴ + 5(10³) + 625 = 10⁴ + 5(10³) + 6(10²) + 25
5[10⁴ + 5(10³) + 6(10²) + 20 + 5] = 5(10⁴) + 25(10³) + 30(10²) + 10² + 25
= 7(10⁴) + 8(10³) + 10² + 25
5[7(10⁴) + 8(10³) + 10² + 25] = 35(10⁴) + 40(10³) + 5(10²) + 10² + 25
= 39(10⁴) + 5(10²) + 10² + 25 = 3(10⁵) + 9(10⁴) + 6(10²) + 25
5[3(10⁵) + 9(10⁴) + 6(10²) + 25] = 15(10⁵) + 45(10⁴) + 30(10²) + 10² + 25
= 10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25
(125)(125²) = 10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25
(25)(125)(125²) = (20 + 5)[10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25]
= 20(10⁶) + 180(10⁵) + 100(10⁴) + 60(10³) + 20(10²) + 500
+ 5(10⁶) + 45(10⁵) + 25(10⁴) + 15(10³) + 5(10²) + 125
= 25(10⁶) + 225(10⁵) + 125(10⁴) + 75(10³) + 25(10²) + 625
= 25(10⁶) + [22(10⁶) + 5(10⁵)] + [10⁶ + 2(10⁵) + 5(10⁴)] + [7(10⁴) + 5(10³)] + 3125
= 48(10⁶) + 7(10⁵) + 12(10⁴) + 5(10³) + 3(10³) + 10² + 25
= 4(10⁷) + 8(10⁶) + 8(10⁵) + 2(10⁴) + 8(10³) + 10² + 25 = 48828125
5¹¹ - 3² = 48828125 - 9 = 48828116
Great 👌 process. Nice 👍 solution.✅
@@hamzagezici1731 thank you. 10^3/2^4 is a very useful ratio to avoid long division by 2048. and indeed, 10^11/2^4 = 5^4*10^7 which is then easier to divide by 2^7
3125×3125×5-9，i think this is more easier. 😂😂
125² =(12 x 13) x 100 + 25. Это - считать по-русски))
too many unnecessary steps. confusing the students.
Genius
Thanks 🙏🙏🙏
I liked his way. It shows he knows algebra thoroughly. I'm sure Stanford has more difficult variations of the same problem.
I'm glad you found it helpful! 🤩💯Thanks for the feedback! 👍💯
A lot of algebra when a calculator is state of the art.
What's the meaning teaching calculating?
This problem becomes much easier if you change base:
5^11 - 3^2 (base 10)
= 100000000000 - 14 (base 5)
= 44444444431 (base 5)
Converting the final answer back to base 10 is left as an exercise for the reader.
Wow. When I saw all the bases and exponents were different prime numbers, I didn't see where to start, though of course was looking for x^2 -- y^2 somewhere.
This was great.
Thanks for your positive vibe🤩🤩🤩
Easier is multiply eleven times the number 5 and then subtract 9 😂
Notice that there is a mistake in calculations. After factoring out 5 and applying the rule of two squares equals sum times difference of squared numbers, you forgot to put it in square brackets. As a consequence you only multiply the first addend of the sum.
Please correct me if I am wrong.
Stanford admissions does not test math. Just submit your application.
Thanks for your comment! 🙏💕🥰✅That's an interesting perspective! 😎🥰✅
You just complicated the problem more. 😅😅😅
I appreciate you sharing your thoughts! 🎉🎁I’m glad you found the video amusing! 💯🙏🤩💕
If you change the five to a seven in the original problem, people won't complain about your solution being more complicated.
I'll do a video in the upcoming upload! Thanks for sharing your suggestion💯🥰✅💪
5x2(3126x1562)-4=10x(3126x1000+3126x562)-4,then 3126x562 can be easier to caculate
It can be solved one third time by simple multiplication
Stan,this is from sthan Arabic and Sanskrit meaning place country village or town Ford English a place of shallow water wet mud or pond . Stanford meaning a shallow water place where university is built.Thank you.
I appreciate you sharing the meaning of Stanford. 🙏🤩🤩🙏😎💕
@superacademy247 Thank you dictionary gives this meaning.
What a waste of time to solve such a simple problem?
It's not simple. Just calculating 5^11 is much more simple, easier and faster.
It's all about simplifying the expression and finding a clever way to represent it.✅💖😊😍
Amerucan universities do not have enterance exams. Good and challenging problems but not an enterance exam.
Why would you do it that way?
I guess that professors in mathematics from Stanford University, learned at secondary school already in "calculator era".
So, they probably do not know about multiplication in column method.
It’s all about logic and problem-solving, not just calculation methods. 👍This problem tests your understanding of concepts, not your calculator skills 😎💯💕🙏
@@superacademy247 Excuse me, if multiplication in column works here faster, let say, it is not the best example of the problem. Should be common sense anyway. And, by the way, how did you get 5^5 so quickly?
5^5 I got it quickly through experience because I'm exposed to numbers daily.
Crazy, on his video he says "no calculations allowed", yet all he is doing is calculations 😂
Good practice.
😍✅
"Calculations not allowed." Well, there were calculations in the video. Repeatedly multiplying by 5 is trivial. Then just subtract 9.
Calculators are not allowed
2. 2
5×961. Not equal with 4805
Just do 3125x3125, one hundred of passages to NOT semplify a multiplication
Imprezionante.
As 5^{11} -3^2 is not large, why not compute directly
5^{11} - 3^2 = 125^3 x 25 - 9 = 15625 x 25 - 9 = 1562500/4 - 9 = 390625-9 = 390616
125^3=1953125 not 15625
The explanation categorizes this as an "algebra problem". Wrong, it is purely arithmetic, not algebraic, since there are no variables present.
Oh I would not consider of Stanford University if calculate by such method 😂
I would like to see some proof that this question, and others like it, were actually posed by reputable bodies. They just don't have the right 'vibe', and look as though they have been invented purely for sites like this one. Academics might well ask, "how would you solve this?". But as soon as one mentioned surds, they would move on to something else and not expect lots of tedious manipulation. Academia ranks insight far above kindergarten arithmetic.
Nice information
Thanks 🤩
一般人從A點慢慢走到B點要走40天，姑姑因為有輕功，所以只要，38天！
3^2=3*3=9
just scroll to 10:48 in the video to get the answer.
Just multiply the numbers and subtract, it seems faster than the method here
Meanwhile Apollo 13 is running out of clean air.
😊
🤩
5^11 is only an 8-digit number, most calculator can do it.
I was hoping for more steps.
इतने समय में तो साधारण तरीके से भी सरल किया जा सकता है।
I prefer a calculator rather than all the manipulations.
"Ridiculous" is a charitable assessment. "Tortured pointlessness" might be closer to it. What a waste.
There is an admission test for Stanford?
It's a hypothetical problem based on the general admission process 😊It's a fun challenge, not a real Stanford test! 😅
3^2=9
Is phoning a friend allowed for standird admission test ?
Don't see the point of doing Algebra here. It would be much quicker to raise 5 to power 11 stepwise and by hand.
5^11-3^2= 11-2=9
I can't see any reason to calculate like this, just calculate 5 by 5, 5^2=25, 5^4=625, 5^5=3125, 5^10 = (3100+25)^2= 3100^2+2*3100*25+25^2=9610000+155000+625=9765625, then multiply by 5 and minus 9. multi-power of 5 should be an easy calculation, the method here is just nonsense.
Todo esto es perder el tiempo ... entonces para que se inventaron las calculadoras...?
Given that 5=10/2,everything else is trivial
Here's what I did:
5¹¹-3²=5³5⁸-3²=5³(5⁸-3²)+5³3²-3²=5³(5⁴+3)(5⁴-3)+5(5²3²)-3²=125(625+3)(625-3)+5(15²)-9
=(1000/8)(628)(622)+5(225)-9=(1000)(628/4)(622/2)+1125-9=(1000)(157)(311)+1116
=(1000)(48827)+1116=48827000+1116=48828116
Awesome 😎💯
自以為聰明，其實在繞遠路
Let him show you how to make an easy one to complicated
Boring: 625x625x125-9=
Why do you have to make it complecsted.
For most of the commentators: this kind of exercise is for testing the imagination, beligerancy and resiliency of the candidate.
So, congratulations, most of you would have passed the test. 😄
Well said! Great point!
No calculation ???
without calculator
5^11= 10^11/2^11= 5x10^10/2^10=25x10^9/2^9=125x10^8/2^8=625x10^7/2^7=3125x10^6/2^6=15625x10^5/2^5=78125x10^4/2^4
=390625x10^3/2^3=1953125x10^2/2^2=9765625X10/2=97656250/2=48828125
5^11-3^1=48828125-10+1=48828116
you just multiplied all fives sequentially which is not overly optimal unless you know higher powers of 5 by heart
Its get long job well done the baby is crying 😂
5^11 - 3^2 = 5^5 * 5^6 - 9
5^5 = 5^4 * 5 = 625 * 5 = 3,125
5^6 = 5^5 * 5 = 3125 * 5 = 15,625
3125 * 15,625 - 9 = 48,828,125 - 9 = 48,828,116 ... ok, might need a pencil to do this multiply
They drag out the solution which is torture for those of us interested in the problem.
Is it really a admition test question ?!😮
Porque siempre se copia el enunciado otra vez?
Which statement?
cARAMBA!!!
I like your solution too.
5^5=5*25^2=5*625=3125
Next, use a trick for squaring numbers that end in 5
5^10=3125^2=(300+12)(300+13)100+25=(90000+7500+156)100+25=9765625
5^11=5*5^10=97656250/2=48828125
Great 👌 trick.🙏🙏🙏
no way this is an admission test, too difficult for most students
This was an actual problem in Stanford's admission test back in 2020 😂.
@@superacademy247which is a shame
It’s in my head
That's nice to know bro.
?
in english the letter "b" is pronounced as in "baby" not as in "papa" ... quite distracting
also "a*b" is not read as "a into b" - rather "a times b" ... quite distracting
5^11 - 3^2 = 25(125^3) - 9
125 x 125 = 12500 + 2500 + 625 = 15625
125^3 = 15625 x 125 = 1562500 + 312500 + 78125 = 1953125
25(125^3) = (125^3)(100)/4 = 195312500/4 = 48828125
5^11 - 3^2 = 48828125 - 9 = 48828116
Unusually Very long procedure.
Yes, you know algebra, but is your point to show us what you know or teach us?
You didn’t simplify anything, just a not easy way to calculate the numbers. While the original problem is also kind of stupid!
Chisanbop that jawn
5^11 = 10^11 / 2^11 = 100,000,000,000 / 2048 = 48828125 then 48828125 - 9 = 48828116
16-5= 11
Can we explain this in 10 minutes??????
А не проще просто посчитать
이정도 문제는 한국에서는 중학교 3학년(미국에서 9학년) 수준 문제이다.
Not a nice solution.
How about using a LOG?