Japanese | A Nice Radical Math Simplification | Math Olympiad

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[@schlingel0017]

There is no need to open the paranthesis of 4th power. You could do the second substition before that.

[@runninggreenhorn9185]

Haven't been doing this for more than thirty years ... and never missed it. 🙂

[@joansola02]

The fourth root would have allowed for an extra simplification, giving 13 as the final result 😊

[@artyonehundred]

169 is 13^2, so is there further simplification to be done at the 8^2 + 7^2 + 8 x 7 stage?

[@villiamo3861]

Excellent. Thank you.

[@saadalikhan9210]

Should've used a^2 + b^2 + c^2 form

[@vpgmiramar]

Nice. Elegant.

[@user-fb1qo8go1b]

Прекрасная задача и великолепное объяснение ее решения. Мне 72 года и моя профессия не связана с математикой, но мне все понятно и интересно. СПАСИБО

[@VincentLauria6]

Surprised he didn’t end it with 169 = 13^2

[@ashokpandey5828]

Nice

[@learncommunolizer]

Thank you very much!

[@udayabose2357]

Why not just long multiply, add, divide by 2 and then find the square root? Much simpler.

[@irinabaigozina8551]

Супер мега задача! Thank you so much for it! It's perfectly cool

[@learncommunolizer]

Thank you very much!

[@terencetwentyman-jones8861]

That would give me writers cramp.....and why would I ever need to do it....

[@user-hq3uj4hx1w]

just calculated in my head and got the result of 169 without draw more than a full papersheet the root of 64 and 49 squared is just 64 and 49 plus 15 squared ist 225 338 half is 169 it was less than 1 minute

[@indigopeach]

Ow! My brain!

[@glennmann634]

Brilliant!

[@unbeaunom]

Cool. I loved it.

[@PatrickCazaux]

Was the first substitution necessary ?

[@bvenable78]

No substitutions are _necessary_; they just make the algebra easier. I like that he did the two substitutions; it breaks the problem down into smaller steps, making it more accessible to viewers - especially those that aren't practiced enough at algebra to follow skipped steps.

[@MathSync]

i ❤ Mathematics

[@himadrikhanra7463]

15× rootover 226..?

[@FedorLyudogovskiy]

169 = 13^2 = 8^3 - 7^3

[@user-pi2my7vk5j]

Математика как Поэзия! Им ночью снятся Арктики и Звездные Галактики, ведь математик- это Фантазёр!

[@matsonnerby]

So much simpler than using a calculator 😂

[@AlenaSlavic]

Легче все перемножить , будет корень из 28561=169.

[@tiramisu00]

±169

[@JoseManuelSosaGarcia]

169

[@stuartcockroft4365]

328

[@fernandopobletebyfepo4820]

Prefiero seguir programando en asembler

[@dhanasekaransundaram4141]

Very nice

[@learncommunolizer]

So nice, Thank you very much!!!

[@oliverdauphin236]

Très astucieux. Bravo !

[@learncommunolizer]

Thank you very much!

[@guptajii7495]

120√2 solution 😢

[@gagwong8964]

Are we not doing √ as the last step to get ±169 as answer?🤔

[@mickaelbazola849]

No, a square of number is positive

[@go_gazelle]

In algebra, the radical sign typically indicates the positive root only. A ± sign in front would indicate both roots. (y = sqrt(x) has no negative values for y.) However, I wouldn't say it's wrong if you include -169 as a second answer. I actually like that since the problem presents as arithmetic.

[@gagwong8964]

Thank you both for clearing my doubt.🙏🏻 I indeed went back to read about the basics . It says something like this : square root of a number is always positive, only in functions or equations like y=x², x has two values, the positive and the negative.

[@go_gazelle]

@@gagwong8964 I think that's basically correct. But y = x² seems like a strange example. A better example would be 9 = x². Here x = ±3. Or a = x². Here x = ±sqrt(a). Whereas, y=x² should be interpreted as a function in which there are infinite values for x.

[@garryjohnson6794]

No, this is too long..sometimes question like this in a test only give you 1 to 2 minutes to solve,.

[@russomarioaa]

Giochi di teoria , con calcolatrice vai subito alla soluzione😊 comunque ottima conoscenza👍

[@kentbrooks3227]

This is why I changed my major to music!

[@loganshaw4527]

College mathematics is just different. I loved exponentials as a kid did not learn of the different elevations until later. I know equal and above but not not learn much of below. But only learned to the end of highschool.

[@dannyroosenboom3640]

sqr30705

[@bs5583]

Haaaaa bic mac

[@vicenteayllonperez2879]

Y no le veo ningún aporte a las matemáticas

[@irenebeltranruiz3431]

Another solution First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169 Can you do without pencil and paper?

[@rcyu]

Don't you have to distribute the square root to 2 as well?

[@gagwong8964]

√(a²+b²+c²) ≠ a+b+c

[@marcherrmann9635]

Pure coincidence?

[@keescanalfp5143]

​@@gagwong8964, in spite of all we see that it still works, at least for her.

[@hongthanhtran9944]

Thanks! Step 6 you lose )

[@gandhimahatma3304]

I’m not advanced by any means but so many unnecessary steps. Neat little arithmetic problem though

[@anatolykatyshev9388]

I have much better solution. Everybody knows that 64^2=4096. 49^2=2401 15^4=225^2=50625 Half sum of it is 28561, which is square of 169, also known fact.

[@Swannerator]

"Everybody knows that..." - tell us that you cheated and used a calculator without telling us that you cheated and used a calculator. 🤡

[@anatolykatyshev9388]

@@Swannerator Author also used calculator to find square roots of 64 and 49. It is not easier , than 64^2 and 49^2!

[@olegkobyzev1884]

⁠​⁠@@Swannerator no need in calculator, that numbers are small (easy to multiply in mind), and even if you not remember 169^2 you can just calculate it on paper.. every one knows

[@maas_ter]

​@@anatolykatyshev9388everyone knows sqrt of 64 and 49 💀

[@gagwong8964]

Concur, way much better than fiddling all that ↑↓←→abxy口O∆ around 🤦🏻‍♂️

[@CyBeatsSs]

Too much steps

[@bvenable78]

I expect he did that for instructional purposes, and to make the solution accessible to viewers with less practice in algebra.

[@Crusader-George]

not really, it's doable compared to sqrt thousands lol

[@comdo777]

asnwer=9 os isit

[@UniqueNewYork27]

Guys, I just took the sqrt and squared exponents and cancel them out, then it'll be 64+49+(15)^2/2 Secondly, 64+49+225/2 Lastly, 338/2 Now you have your answer of 169, i didn't even learn this at school yet💀

[@phoebe543]

The denominator wasn’t squared

[@Swannerator]

I hope you pay attention in Maths class when your class gets up to this. 🤦🏻‍♂️

[@UniqueNewYork27]

I didn't even learn this at school yet lol

[@popolaminc6188]

🤦‍♂️Unexplainble, but you got the right answer

[@irenebeltranruiz3431]

I did the same!

[@MrPizzaHut]

The square root sign cancels out the x² (squared) signs and reduced the x⁴ to x² so the final equation before you solve is: (64+49+15²)÷√2=274+10140+101400=101814÷2=√50907=225

[@ughtht-gnicuitnck]

√50907=149

[@gato_catindig]

i just removed the squares and made 15^2/2 i got the same answer lol

[@grafeebabee]

why not first get rid of the square root bracket by reducing the numbers to 64 +49+15^2...add those then divide by 2 and you still get 169 and the square root of that is 13....

[@alexgrebenschikov4638]

Toooooo long solution

[@RobbieIsbell]

WFT? I DID IT IN 3 STEPS. 169

[@marcherrmann9635]

Elaborate further, please....

[@RobbieIsbell]

@@marcherrmann9635 Seriously? It's easy: First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169

[@brunobastos5533]

I never understand why they add so many steps . Like all numbers are 2 or power of 2. They do it like pc's not stray from the way they learned it even if the solution is infront of them

[@willys2747]

This isn’t real math. It’s nothing more than merely recognizing patterns.

[@KW-fb4kv]

This is a terrible question. Useless maths that not only teaches kids very little , but misleads them into thinking they should memorize the tree for (a+b)^n expansion. Memorization lacks mathematical elegance

[@francoistrotier6145]

C'est pas 169. C'est 225.... (2x56) C'est pas 13 au carré mais 15 au carré..... Un peu de sérieux svp.

[@user-rw9cm9hk7m]

Le résultat final est bien 169.

[@gerardphilippe5793]

Une fois 56. Pas deux fois. C'est donc bien 169. Et pas 225

[@unbeaunom]

C’est souvent ceux qui reprennent les autres qui se trompent. Il faudrait formuler ceci en une équation.

[@matbohman]

Non. b = xy (pas 2xy).

[@Crusader-George]

you're wrong

[@bobjensen4051]

Finally, it.equals 13.

[@bvenable78]

Why are you taking the square root of his final answer?

[@unbeaunom]

Joke?