A Nice Square Root Math Simplification | No Calculator 📵 | Math Olympiad |You Should Know this Trick

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[@waninazirahmad3792]

a2 +b2 -2ab =(a_b)2 not (a+b)2

[@Nikioko]

√(√25 - √24) = √(5 - 2√6) = √(3 - 2√3√2 + 2) = √(√3² - 2√3√2 + √2²) = √(√3 - √2)² = √3 - √2

[@mach1553]

Nice ASCII math figures, thanks!

[@davidwright8432]

Eh? at 4.02 you say (a + b)^2= a^2 + b^2 - 2ab. Surely that should be +2ab ?

[@TheMathScholar23]

Yeah, that was a typo and I fixed that in the next line after a while

[@boabnr418]

That is 8 grade' russia problem huh sqrt(5-sqrt(24)) a²+b²=5 2ab=2sqrt6 a²+b²=5 ab=sqrt6 it is obvious that they can be sqrt3 and sqrt2 as sqrt2×sqrt3=sqrt6 2+3=5 So sqrt3-sqrt2

[@SP-224]

That's what I was thinking I studied in middle school n as far as i remember it should be (a-b)^2 =a^2-2ab+b^2.

[@HoSza1]

Kill not only two but MANY birds at once. Theorem: √(x±√(x^2-1)) = √((x+1)/2)±√((x-1)/2). Substitute x=5. √(5±√24) = √3±√2. Done. √3+√2 is a fun approximation of 𝜋 btw 😂 A more general form of the same theorem: √(a+b±2√ab) = √a±√b. Here you can choose a=3, b=2 to get the same result, for example.

[@Misteribel]

Though the solution is not +/-, it's only minus, not plus (but I'm sure you're aware).

[@HoSza1]

@@Misteribel You are right, for the problem presented in this video, only one of the signs is correct, and I tried to solve a more general form, where either of the signs can be chosen as fixed throughout the same solution.

[@Sg190th]

1.7 - 1.4 so it should be approximately 0.3 or close to it.

[@Ramkabharosa]

√{a ± b√c} (a,b,c non-neg. rat. nos.) can be simplified to √y ± √z iff {a² - b².c} = d². If this d exists, then take y=(a+d)/2 & z=(a-d)/2. Here a=5, b=1, & c=24. So d = √{5² - 1².(24)}= √{25 - 24} = 1. So y=(5+1)/2=3 & z=(5-1)/2=2. ∴ √{5-√24}=√y-√z=√3-√2. .

[@RedStarMapping]

Absolutely brilliant!

[@stephenhenley7452]

Isn’t the square root of 25 also negative 5?

[@TheMathScholar23]

No

[@xation6048]

Even if that was the case, the inside of the whole sqrt wouldve been a negative number making the solution complex. I dont think thats what we're looking for here

[@harrymatabal8448]

Stephen √25 = 5 only

[@PENSILEDK]

No

[@Misteribel]

There are many videos explaining the concept and why. The sqrt symbol returns the *principal square root* by definition.

[@thefox1703]

Very clever!

[@misterenter-iz7rz]

(r2 +r3)^2=5+2r6=r25+r24, so the answer is r2+r3.😊

[@TheMeefive]

I don't get it.

[@Ed19601]

Easier method sqr24 is about 4.9 (a fraction less) hence we are left with sqr0.1 which is 0.33 but we need a bit less (as it was a fraction less) so 0.32 "Yeah but you did not calculate it, you estimated it", well, it still is a precise answer and more meaningful than sqr3-sqr2

[@subhrapal692]

You don't know the formula well

[@tcmxiyw]

This is called denesting.

[@maratzhamanbalanov7511]

Thank you! Nice decision 🎉

[@deepaksingh-fh8hu]

I solved in just 3second

[@instafuny]

Some false. Coz how fix squre without removing squre root? Its nagative

[@jagdishk1591]

Nice presentation.

[@johnlamb3101]

What a looooooong winded way of working this out. Get to the answer quicker

[@bobbyheffley4955]

Binomial theorem

[@alter.007]

Вау, круто! :)))))

[@jean-paul4337]

Bravo!

[@jean-paul4337]

Bravo!

[@padmavati5974]

This is (a-b)2

[@MyNordlys]

Yes, there is this error in the vidéo.

[@abrahammelkonian9698]

amazing

[@lawolffamily]

Lol, il se trompe et il ne refait pas une nouvelle vidéo....:):):)

[@BrunoPessolani]

The answer is 3(square root)-2(square root)

[@anotherelvis]

NIce trick

[@ThanhVo-nz8nv]

Sai dấu rồi ( a-b)tất cả bình

[@sabrewolf4129]

Another long winded explanation for a simple equation. Why can't these videos just get to the damn point instead of getting a hard on listening to themselves speak?

[@harrymatabal8448]

I totally agree sabre

[@SrinivasuluMandapati]

Formula return by you is wrong

[@FerderSBV]

.10

[@tonyshilson9901]

1

[@ganeshdas3174]

Go for ✓3-✓2= 0. 318

[@ramshekhar3906]

फार्मूला गलत लिखा जा रहा है

[@Jorick_73]

Надоели уже задачки такого типа. Всегда очевидно, что надо избавляться от внешнего радикала и искать полный квадрат, подбирая каждый из компонентов как корень квадратный из какого-то целого числа. В принципе это задача на полный перебор вариантов. Тоска смертная. Решил за минуту, гораздо компактнее! Получил sqrt(3) - sqrt(2). Ну и на кой чёрт это нужно? Все равно, если надо будет искать точное численное решение, то без калькулятора не обойтись, а в исходной формуле sqrt(5-sqrt(24)) будет столько же вычислительных операций, что и в "упрощенной" формуле.

[@Misteribel]

Why "the same number of ops?"? The original has a nested root, the result doesn't, plus the operands are much lower, i.e., computationally a magnitude difference. It's common to simplify expressions in math and this one is trivial, so you should do that. And as to your comment on "exact numerical solution", it doesn't exist, so a calculator is useless either way (it was odd of the youtuber to say so).

[@Limited_Light]

Yes, not only is there one less step in approximating, but also yes that with smaller numbers even a calculator should "find it easier" to approximate with smaller numbers and one less step. @@Misteribel

[@harrymatabal8448]

Excellent explanation.thanks

[@richdobbs6595]

Why would you post this without re-recording it to remove your mistake?

[@darkmader3898]

Math is ridiculous. Either you're born to do it or you're not. You can not learn this out of simple curiosity or interest.