Left side: combine powers of fractions until you get 5 to the power of 7/8. On the right side, 125^x is the same as 5^3x. 3x = 7/8; x = 7/24. You can also do it by reducing fives until you get 5^(3.5 -12x) = 1, then 3.5-12x = 0, x = 3.5/12, which is the same result
@@bertblankenstein3738He rewrited many time with the aims : to all kinds of the viewers who had watched this video. I think he is a good man when he did so.Tks!
20 years ago as an engineering student and probably one of the best times of my life, I could just zip through this equations. Thanks for the memorys. NorCal
@@MathsExplorer24 It's not the method; it's the speed. I think you could present this clearly in 3 or 4 minutes instead of 10 simply by being more efficient.
@@berkeleyrc That's how I did it in my head very quickly as well. I do like to see how other people solve things though, shows how different brains work. As a former math teacher, I appreciate someone who shows all their steps as well
1/write correctly seven instead 1 2/the task can also be easily calculated from the last root on the right to the largest root without square very quickly!Try!
If you do the sqrt2 maths it is easier and faster, you can do it in your head then. You will have 5^7/8 = 125^x then power to 3 or sqrt3 you will get with power 3, 125^7/8 = 125^3x then 7/8 = 3x and x= 7/24
These problems seemed like a headache and nightmare during school days but now it is ok. Thanks to the patience which I have gathered over the years...
I went with the second method because that is more easier logical way to see it and faster if you are not prepared to do the first way. So I spent a lot of time doing it in my head without any paper and pen and I came to the right answer. Then I saw that your video continued. 😢😊
Four parts to a square the center 25 would be the one in the center of the square can you have a 125 X found extending for an extra 25 in a square root |__|square ruot
Where there any of those square/ root operations that could have had a +/- answer? Like sqrt(25) can be -5 as well. Maybe with the operations involved it doesn’t matter. But could this have two correct answers?
5 is a positive number, so the square root of 5 has only one positive answer. In the case, for example x^2 = 4 ==> x = + 2 or x = - 2 ( two answers ) because we don't know exactly x is a positive or a negative number. We have to choose both + 2 and -2 .
@@pnwtutoring No. The square root of 5 can be either positive or negative. Either way, it an irrational number, but using approximate values, (-2.236) x (-2.236) = +4.999696.
@@arjanhulsebos No. Square root is a function that you apply to a number and it has 2 values, one positive and one negative. According to Wikipedia "Every positive number x has two square roots".
@@chrisengland5523your problem isen't really a mathematical problem: Mathematician just defined that sqrt(5) ist just the positiv solution of 5=x^2. So formally the solution of 5=x^2 ist sqrt(5) and -sqrt(5), not just sqrt(5). If wiki says different then it is wrong. Btw. the reason why it is defined like that to keep sqrt(x) beeing a function (mathematic function, not same like an function you know from programming), which makes it easier to handle. So after the formal definition of sqrt there arent more solutions. But actually there is a related Problem happening while solving that equation: squaring the equation leads to possible inproper results, which makes the verification at the end necessary.
During verification, separately solve LHS and RHS, because when you put an = sign from the beginning, it states that they are equal, so there is no need for verification. Hope you understand what I'm trying to say.
Brilliant video, however think a longer form with voice audio explaining this would be little more helpful. Just watching you right this out meant nothing to me. But I would love a better explanation how this was solved
@@elenaterskova6422 а ещё быстрее завести множитель под знак корня, слева будет корень шестой степени, а потом же и возводить в шестую степень левую и правую часть.
Not 'a bit unnecessary' but totally unnecessary. These so-called YT maths teachers have no insight and no artistic feeling for mathematics. All they can teach is low-grade drudgery for unthinking students.
Personalmente avrei seguito un metodo più semplice. Avrei trasformato le radici di sinistra raggruppando tutti i 5 e a destra avrei scomposto il 125 nei suoi numeri primi ottenendo √√√5^7=5^3x 5^(7/8)=5^3x 3x=7/8 X=7/24
I thought for sure I aced algebra when I took my first test. The teacher failed me because I answered every problem with an "X" I thought "X" was the unknown. The answers were unknown to me.
How the heck can this be useful. I'm a 60 year old linguistics professor that has travelled and lived all over the world. I was a paratrooper for 15 years. I've never had any occasion in which something like this had any relevance. I've built bridges, and shelters without any of this. How is it not a waste of time?
Algebraic thinking teaches people to solve problems by logical step-by-step methods. This is a skill the world could use more of in my opinion. As far as encountering the square root of a square root of a square root, that's probably not going to happen 😂
Left side: combine powers of fractions until you get 5 to the power of 7/8. On the right side, 125^x is the same as 5^3x. 3x = 7/8; x = 7/24. You can also do it by reducing fives until you get 5^(3.5 -12x) = 1, then 3.5-12x = 0, x = 3.5/12, which is the same result
это решение проще и быстрее.хотя я по английски ни бум бум.но решение на поверхности.к тому же многократное возведение в квадрат не желательно,
That's what I did!
👌🏻👌🏻
Я тоже степени приводил к ⅞. Так намного проще и быстрее
7/8 how to reduce...?
Finished school 58 years ago. It's fun to review watching though some commenters show shorter ways. Thanks you all.
Sou can simplify the left side as 5 raise to power 7/8 and the right side as 5 raise to power 3x and equate them to get the required answer.
Hint. Solve by inspection. Or Log5 both sides.
And this would take about one minute to do. No need to rewrite so many times.
@@bertblankenstein3738He rewrited many time with the aims : to all kinds of the viewers who had watched this video. I think he is a good man when he did so.Tks!
Just square it 3 times.
LHS becomes 5⁷.
RHS becomes 125^8x = (5³)^8x = 5^24x.
So x = 7/24.
Just a few seconds in mind.
where did you get that 7 from?
@@alejandropulidorodriguez9723 square three times
D'accordo
@@alejandropulidorodriguez9723 Square it 3 times. LHS becomes 5^4*5^2*5^1=5^(4+2+1)=5^7
LHS=7/8 as the power of 5. It is not 7, just check your process again
For the impatient, set the playback speed to 2x.
And for the "normal" folk, use 3x.
5^7/8 =5^3X 3X=7/8, X=7/24
Could have been done much simpler like you said, so much wasted time... And this music....
5 7/8'e nasıl ulaşıldı? Yöntem nedir?
Vas introduciendo dentro de la raíz
@@alkara21 square root of x can be written as x to the power 1/2
@@alkara21 5^((((1/2+1)/2)+1)/2)=5^(7/8)=5^(3x) => 7/8=3x => x=7/24
20 years ago as an engineering student and probably one of the best times of my life, I could just zip through this equations. Thanks for the memorys. NorCal
Don’t spend the first thirty seconds rewriting the question.
@@MathsExplorer24 It's not the method; it's the speed. I think you could present this clearly in 3 or 4 minutes instead of 10 simply by being more efficient.
Honestly it took me just a few seconds:
sqrt(5*sqrt(5*sqrt(5))) = sqrt(5)*sqrt(sqrt(5))*sqrt(sqrt(sqrt(5))) = 5^(1/2)*5^(1/4)*5^(1/8) = x^(7/8)
@@berkeleyrc That's how I did it in my head very quickly as well. I do like to see how other people solve things though, shows how different brains work. As a former math teacher, I appreciate someone who shows all their steps as well
@@MathsExplorer24For the elementary schoolers.
@@MathsExplorer24it’s not. It’s already written down. That makes as much sense as writing the same thing 2 more times. Or 3, or 4. It’s not a step.
Very well explained,had forgotten my maths after 50 yrs
1/write correctly seven instead 1
2/the task can also be easily calculated from the last root on the right to the largest root without square very quickly!Try!
Bonjour, Je remplace toujours la notation" racine carrée" par "puissance 1/2". C'est toujours plus simple. Merci pour cette démonstration.
simple and detailed. congratulations. good video ❤
👌🏻👌🏻
Square 5 equals y so y elevated by 7/4 equals y elevated by 6 elevated by x. 7/4lny equals 6x lny . So 7/4 equals 6x. X equals 7/24 equals 0.291667
The exact answer is 7/24. Decimal number is called an approximate learn the difference.
Excellent way of doing and steps. I am a non maths teacher but understood your steps easily. Thankyou and hope you would send more
If you do the sqrt2 maths it is easier and faster, you can do it in your head then.
You will have 5^7/8 = 125^x
then power to 3 or sqrt3
you will get with power 3, 125^7/8 = 125^3x
then 7/8 = 3x
and x= 7/24
Or just rewrite the left hand side in a few steps as a 5 exponential, then
5^(7/8) = 5^3x
3x=7/8
x = 7/24
Would also say that is the faster solution. Actually he used that way for verifying his result.
I returned to my schoolhood appr. 55 years ago. Thanks. 🍀
How is a question like this applied to real life situation
@@SandraDevant …it means I love this maths min. 55 years.
@@SandraDevant It depends: if your "real life situation" is being a cheap uneducated labour OR something more than that 😊
😁👌🏻
Very good presentation 👍
Excelente .Muito Obrigado . De Portugal
Very good explanation sir.... 😊
I managed to get some sleep. I deliberately lengthened the video to increase monetization. The problem is solved in the mind.
👍🏻
Very good
Nice presentation
Simple explanation that I enjoyed reviewing my past knowledge from 35 yeras ago!
Make me feel interesting in maths. Thanks.
it is interesting. I kept squaring to get rid of the square root. then the problem is transformed like 5^7=5^(24x). so x=7/24. thank you~~~
Very beautiful.....
So clear! Thanks!
Good question 😍
Nice explanation
These problems seemed like a headache and nightmare during school days but now it is ok. Thanks to the patience which I have gathered over the years...
Very much enjoyed.
So enjoyable, a very thorough and systematic work.
Why not just use the fractional exponents and get to the answer in half of the steps and less math along the way?
👌🏻👌🏻
Nicely done!
Out standing, thanks.
Very interesting
👌🏻👍🏻
My, my, you did it the hard way.
Nice calculation
Gostei! Até parece que é falta do que fazer. É gosto pela arte.
Good.
Sweet proof!😀
Good problem actually was fun thanks for taking time tough to remember steps lol when u r old like me 😅
I went with the second method because that is more easier logical way to see it and faster if you are not prepared to do the first way.
So I spent a lot of time doing it in my head without any paper and pen and I came to the right answer. Then I saw that your video continued. 😢😊
Amazing🙏👏👏many thanks!
تمرين ممتاز وشرح جيد والتححق من الحل ممتاز
Four parts to a square the center 25 would be the one in the center of the square can you have a 125 X found extending for an extra 25 in a square root |__|square ruot
Thanks for this very good vidéo 👍
வீர லெவல்
Where there any of those square/ root operations that could have had a +/- answer? Like sqrt(25) can be -5 as well. Maybe with the operations involved it doesn’t matter. But could this have two correct answers?
5 is a positive number, so the square root of 5 has only one positive answer. In the case, for example x^2 = 4 ==> x = + 2 or x = - 2 ( two answers ) because we don't know exactly x is a positive or a negative number. We have to choose both + 2 and -2 .
@@pnwtutoring No. The square root of 5 can be either positive or negative. Either way, it an irrational number, but using approximate values, (-2.236) x (-2.236) = +4.999696.
@@arjanhulsebos No. Square root is a function that you apply to a number and it has 2 values, one positive and one negative. According to Wikipedia "Every positive number x has two square roots".
@@chrisengland5523your problem isen't really a mathematical problem: Mathematician just defined that sqrt(5) ist just the positiv solution of 5=x^2. So formally the solution of 5=x^2 ist sqrt(5) and -sqrt(5), not just sqrt(5). If wiki says different then it is wrong.
Btw. the reason why it is defined like that to keep sqrt(x) beeing a function (mathematic function, not same like an function you know from programming), which makes it easier to handle.
So after the formal definition of sqrt there arent more solutions.
But actually there is a related Problem happening while solving that equation: squaring the equation leads to possible inproper results, which makes the verification at the end necessary.
Brillant
During verification, separately solve LHS and RHS, because when you put an = sign from the beginning, it states that they are equal, so there is no need for verification. Hope you understand what I'm trying to say.
Brilliant video, however think a longer form with voice audio explaining this would be little more helpful. Just watching you right this out meant nothing to me. But I would love a better explanation how this was solved
Masterfully done.
I did this in my head and it took about 20-30 seconds. 9 minutes, jeez
👏👏👏👏
your X is like multiplication symbol. use small x to avoid confusion
Or log 5^{7/8) divided by log 125!
Super bro
I see your vids and I wonder: “how many meters down is your paper?”
Just kidding. Nice work!
Beautiful
5^(7÷8)=5^(3х)
7÷8=3х
х=7÷24
1/2 + 1/4 + 1/8 = 3х, done
Решается в уме за пару минут)
Как?
@@elenaterskova6422 представляешь корни как степени со скобками и 125 приводишь к степени с основанием 5. Дальше очевидно.
@@elenaterskova6422 а ещё быстрее завести множитель под знак корня, слева будет корень шестой степени, а потом же и возводить в шестую степень левую и правую часть.
Sweet
good music.
Hence try to do some calculation at the back of your head
Lengthy procedure
A bit unnecessary, wasn’t it? I just squared the equation 3 times, getting 5^7 = (5^3x)^8 = 5^24x. Hence 24x = 7…
Not 'a bit unnecessary' but totally unnecessary. These so-called YT maths teachers have no insight and no artistic feeling for mathematics. All they can teach is low-grade drudgery for unthinking students.
Here’s easier way
After u know that 5=125^8x-2 and 125=5^3
So its 5=5^3(8x-2)
5^1=5^24x-6
Then 1=24x-6
So X = 7/24 🎉🎉
How did I found on my head 1/4 at first lol 😂
I go with 125.25.5=5^24x
√5×√√5×√5=125powerX. V5×5 ,ie,√x×√x=x. 5powe1=(5×5×5) power x. 5 power 1 =5 power x. Hence x=,1 (ie, both side base equal ie here 5.) Ans x=1.
With a scientific calculator this goes faster by taking ln of both sides.
Took too long.
Just square both sides three times and express the right hand side in terms of 5.
Lastly, compare the exponents.
Lengthy process.
By verification method also we can solve more quickly.
А почему нельзя было сразу 5^7/8=5^3х отсюда 3х=7/8 и х=7/24. По сути всего 2 шага. Это же короче.
24 7 don’t stop enjoying math!!!
😁
Personalmente avrei seguito un metodo più semplice. Avrei trasformato le radici di sinistra raggruppando tutti i 5 e a destra avrei scomposto il 125 nei suoi numeri primi ottenendo
√√√5^7=5^3x
5^(7/8)=5^3x
3x=7/8
X=7/24
Haga un vídeo y nos lo explica paso a paso muy didácticamente. Gracias
Some Mathematicians love to make things complex. 7/8=3x tthen x=7/24. That's all no need more more texts
Si mi amor❤️
I thought for sure I aced algebra when I took my first test. The teacher failed me because I answered every problem with an "X" I thought "X" was the unknown. The answers were unknown to me.
Tnx so much
Задача для устного счета для получения минимальной положительной оценки.
Это уравнение решается на раз, два за пару минут, примените свойство степени.
This X was left in school and college now it is on RUclips. X is still a Mistry 😂😂😂
👍 와
5^7/8=5^3x
7/8=3x
X=7/24
Если бы не громкая музыка, все отлично
How the heck can this be useful. I'm a 60 year old linguistics professor that has travelled and lived all over the world. I was a paratrooper for 15 years. I've never had any occasion in which something like this had any relevance. I've built bridges, and shelters without any of this. How is it not a waste of time?
Im really very weak in maths.. May help this channel think so thanks. 43 yrs old house wife.. Granny also mom for 10 th std daughter. ☝
Bro really spent 10 minutes for this💀💀💀💀
The ans can be 1/2 too
X hai ya multipy
很好。
Please do it faster
Why not use exponent rules. Shoulsnt take that long
What is "Math"?
解題方法太麻煩 把根號化成指數 很簡單，就能解題
Good but where in real life one could use this and how?
Algebraic thinking teaches people to solve problems by logical step-by-step methods. This is a skill the world could use more of in my opinion. As far as encountering the square root of a square root of a square root, that's probably not going to happen 😂