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
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.
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.
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...
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.
Multiplying by 5 is pretty much the same as dividing by 2, just ignore the decimal point. This is how I would solve it: 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 - 9 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
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 =....
625^2=(62×63)25=>
62x63=60^2+60+61+61+62+62=3906=>
625^2=390625
390625×125=390625×1000÷8
390625000÷8=48828125
5^11 - 9=48828125-9=48828116
Video is much more "simplified" as per ask
Takes less time to just multiply out the numbers.
Thank you! I did it in at most 3 minutes.
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.
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! ✅
There is no one best way to do this problem. But with no calculator, I chose 100,000,000,00 ÷ 2048 - 9
Riduculous. Making a meal of an extremely simple problem.
Explains why Stanford is down the tubes?
They are woke and ElGeeBeeTeaWue.
@@dalepeters4927
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.✅
Nice solution but too long . There are shorter ways.
10^11÷2^11-9
1000÷16=62.5
10^8×62.5=6250000000
6250000000÷128=4882825
48882825-9=48828116
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🤩🤩🤩
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...
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
too many unnecessary steps. confusing the students.
What's the meaning teaching calculating?
Easier is multiply eleven times the number 5 and then subtract 9 😂
5x2(3126x1562)-4=10x(3126x1000+3126x562)-4,then 3126x562 can be easier to caculate
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.
The explanation categorizes this as an "algebra problem". Wrong, it is purely arithmetic, not algebraic, since there are no variables present.
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.✅💖😊😍
Just do 3125x3125, one hundred of passages to NOT semplify a multiplication
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
Multiplying by 5 is pretty much the same as dividing by 2, just ignore the decimal point. This is how I would solve it:
5
25
125
625
3125
15625
78125
390625
1953125
9765625
48828125 - 9
48828116
wow.
😊
🤩
Imprezionante.
Good practice.
😍✅
Nice information
Thanks 🤩
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
5^11^1 ➖ 3^1 5^1^1 ➖ 3^1 1 ➖ 3^1 3^1 (x ➖ 3x+1).
इतने समय में तो साधारण तरीके से भी सरल किया जा सकता है।
5^11 is only an 8-digit number, most calculator can do it.
Given that 5=10/2,everything else is trivial
Just multiply the numbers and subtract, it seems faster than the method here
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!
😊😊😊😊😊, THE SOLVED AS YOUR COUNTING , HOW IS IT FOR UNIVERSITY?!😊
Is phoning a friend allowed for standird admission test ?
Let him show you how to make an easy one to complicated
Its get long job well done the baby is crying 😂
5^10*5-5-4=5(5^10-4)
They drag out the solution which is torture for those of us interested in the problem.
Todo esto es perder el tiempo ... entonces para que se inventaron las calculadoras...?
Why so complicated ？ You won’t pass the test if you spend so much time solving this simple question.
Unusually Very long procedure.
3^2=9
Décomposition en base 10 vow
It’s in my head
That's nice to know bro.
312 * 313 =97,656
5^10 =97,65,625
(Just add 25 in end )
97656250/2 =4,88,28,125
This is 5^11
Boring: 625x625x125-9=
rối rắm, quá chậm, cần lấy 5^5. 5^5. 5 là xong
Chisanbop that jawn
Why do you have to make it complecsted.
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! 😅
5^11-3^2= 11-2=9
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! 🔥 💯
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.🙏🙏🙏
Can it be so easy? Stanford seemed nerfed.
No calculation ???
Porque siempre se copia el enunciado otra vez?
Which statement?
i get loose too long
5 * 5 * 5 * 5 *5 = 3125 not calculator allowed 😂😂🤣🤣
This seems…awful? Easer to just multiply it out.
Lol..classic example of how to overcomplicate a problem!!
49
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.
use a calculator! no need to spend that much time
5^11=625*625*125= ((62*63*100)+25)*1000/8 =390625000/8=
48828125
(5^11)-9=48828116
Un calcul direct va encore plus vite. C'est stupide comme question.
계산기로 그냥 11번 곱하는게 빠르겠다 ㅡㅡ
Задача 9 класса Советской Школы.
4,999,991?
It seems not best answer
참 어지럽게 문제푸네~ 암산으로 3초면 풀수있는 문제~
Not satisfied
Please write with a spidol, I can't see your writing
这个思路有点奇怪
문제가. 어렵다기보다
드럽다
풀이가 복잡함
Total ridiculous solution!
What a stupid solution you have given
Stupid problem
Are bhadu
This question is sooo dumb.
But educational
걍 곱해라 뭔 헛짓이냐
咁都叫入大學題目😂，無聊。中三都識
Third grades are NOT exposed to exponents and logarithms
5^5=3125
3125*3125=9765625
9765625*5=48828125
48828125-9=48828116
3125^2
=(3000+125)^2
=9000000+750000+10000+5000+625
=9765625
Why “smart” people want to make simple things complicated to show its “smart “😂
化簡為繁
So it is not calculation!?😂🎉😂🎉
Crying matter
No. Just multiply the freaking numbers. 15625*3125 - 9
搞笑嗎🤪？