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
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.
@@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
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.
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.
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.
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.
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
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.
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
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 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?
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 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.
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
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
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😂
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! ✅
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. 🚀🙏✅👏
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! 💯🙏🔥
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 .
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...)?
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! 👍💯
Totally agree with everyone else. Much quicker and easier to just multiply the numbers out from the word go.
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 😁
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))
Great lesson is the variety of techniques available in solving these types of problems. Thank you!
penjelasannya dibuat rumit..padahal sangat mudah, menit 10:48 = 3.16 x 3.124x5 -4 = 48.828.116
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...
Easier is multiply eleven times the number 5 and then subtract 9 😂
just scroll to 10:48 in the video to get the answer.
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.
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🤩🤩🤩
What's the meaning teaching calculating?
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💯🥰✅💪
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.
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.
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
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.✅💖😊😍
Good practice.
😍✅
If you still have to remember 5^5=3125 and you can only simplify the calculation, then just use a computer to do it.
Crazy, on his video he says "no calculations allowed", yet all he is doing is calculations 😂
Nice information
Thanks 🤩
too many unnecessary steps. confusing the students.
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.
5x2(3126x1562)-4=10x(3126x1000+3126x562)-4,then 3126x562 can be easier to caculate
Meanwhile Apollo 13 is running out of clean air.
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！
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
"Calculations not allowed." Well, there were calculations in the video. Repeatedly multiplying by 5 is trivial. Then just subtract 9.
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
Imprezionante.
Amerucan universities do not have enterance exams. Good and challenging problems but not an enterance exam.
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 😎💯
I was hoping for more steps.
The explanation categorizes this as an "algebra problem". Wrong, it is purely arithmetic, not algebraic, since there are no variables present.
Just do 3125x3125, one hundred of passages to NOT semplify a multiplication
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 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.
😊
🤩
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
इतने समय में तो साधारण तरीके से भी सरल किया जा सकता है।
"Ridiculous" is a charitable assessment. "Tortured pointlessness" might be closer to it. What a waste.
Its get long job well done the baby is crying 😂
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!
2. 2
5×961. Not equal with 4805
Oh I would not consider of Stanford University if calculate by such method 😂
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
Is phoning a friend allowed for standird admission test ?
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
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! 😅
Unusually Very long procedure.
Is it really a admition test question ?!😮
Just multiply the numbers and subtract, it seems faster than the method here
5^11 is only an 8-digit number, most calculator can do it.
Let him show you how to make an easy one to complicated
Given that 5=10/2,everything else is trivial
3^2=9
It’s in my head
That's nice to know bro.
Stanford admissions does not test math. Just submit your application.
Thanks for your comment! 🙏💕🥰✅That's an interesting perspective! 😎🥰✅
cARAMBA!!!
自以為聰明，其實在繞遠路
5^11-3^2= 11-2=9
Todo esto es perder el tiempo ... entonces para que se inventaron las calculadoras...?
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.
You didn’t simplify anything, just a not easy way to calculate the numbers. While the original problem is also kind of stupid!
Porque siempre se copia el enunciado otra vez?
Which statement?
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.🙏🙏🙏
Boring: 625x625x125-9=
Why do you have to make it complecsted.
이정도 문제는 한국에서는 중학교 3학년(미국에서 9학년) 수준 문제이다.
They drag out the solution which is torture for those of us interested in the problem.
16-5= 11
Chisanbop that jawn
Can it be so easy? Stanford seemed nerfed.
I didn't know you had to solve such stupid questions in this university. Thanks. I won't apply for admission now.
Thanks for your feedback! 💖💯I’m glad you found it helpful! 🔥 💯
Décomposition en base 10 vow
Don't see the point of doing Algebra here. It would be much quicker to raise 5 to power 11 stepwise and by hand.
Method 1
------------------
x= 5¹¹ - 3²; u=5¹¹ et v=3²
u=5¹¹
u=5³(5⁸)
u=(125)(5⁴)²
u=(100+25)(625)²
u=(10²+25)(600+25)²; a=25
u=(10²+a)(10²6+a)²; b=(10²6+a)²
u=(10²+a)b
/////////////////////////////////////////////////
b=(10²6+a)²
b=10⁴36+2(10²6)(25)+a²
b=10⁴36+(10²6)(10¹5)+a²
b=10⁴36+10⁴3+a²
b=10⁴(36+3)+a²
b=10⁴39+a²
//////////////////////////////////////////////////
u=(10²+a)b
u=(10²+a)(10⁴39+a²)
u=10⁶39+10²a²+10⁴39a+a³
u=10⁶39+10⁴39a+10²a²+a³
u=10⁶39+10⁴39(25)+10²a²+a³
u=10⁶39+10⁴(40-1)25+10²a²+a³
u=10⁶39+10⁴(10³-25)+10²(25)²+a³
u=10⁶39+10⁴(975)+10²(625)+a³
///////////////////////////////////////////////////
a³=a²a=25²25=(625)(25)=(600+a)a
=>a³=10²6a+a²=10²3(2a)+625
=>a³=10²3(50)+625
=>a³=10³15+625
=>a³=15'625
/////////////////////////////////////////////////
u=10⁶39+10⁴975+10²625+15'625
u=39'000'000+9'750'000+10²625+15'625
u=48'750'000+62'500+15'625
u=48'812'500+15'625
u=48'828'125
and
v=3² => v=9
Then,
x=u - v
x=48'828'125 - 9
Therefore,
x=48'828'116
Method 2
------------------
x=5¹¹ - 3²; u=5¹¹ et v=3²
u=5¹¹
log(u)=log(5)¹¹
log(u)=11log5; log5 ≈ 0,7
log(u)≈11(0,7)
log(u)≈7(1,1)
log(u)≈7,7; 7u>10⁷
u≈10⁷[10^(0,7)];
log5≈0,7 10^(0,7)≈5
u≈10⁷5
and
v=3² => v=9
then,
x= u -v
x≈ 10⁷5 -9
x≈ 50'000'000 -9
x≈ 49'999'991
Method 3
----------------
x= 5¹¹ - 3²; u=5¹¹ et v=3² (v= 9)
u=5¹¹
table 5ⁿ
n=1 ---> 5
n=2. ---> 25
n=3. ---> 125
4. 625
5. 3125
6. 15625
7. 78125
8. 390625
9. 1953125
10. 9765625
11. 48828125
=> u=48'828'125
then,
x= u -v
x= 48'828'125 - 9
therefore,
☆ x= 48'828'116
Why so complicated ？ You won’t pass the test if you spend so much time solving this simple question.
Not a nice solution.
How about using a LOG?
312 * 313 =97,656
5^10 =97,65,625
(Just add 25 in end )
97656250/2 =4,88,28,125
This is 5^11
5 * 5 * 5 * 5 *5 = 3125 not calculator allowed 😂😂🤣🤣
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
No calculation ???
49
i get loose too long
그냥 계산하는 것이 빠르겠다
rối rắm, quá chậm, cần lấy 5^5. 5^5. 5 là xong
Seems complicated than just multiply the numbers haha
I don't think they didn't know that one can multiply numbers out. They want to know that ome is able to manipulate such equations.
Lol..classic example of how to overcomplicate a problem!!
This is grade 9
Задача 9 класса Советской Школы.