Math Olympiad | Can you solve this ? | Simplify Square Root Problem

This is an interesting question with amazing concepts!
Hope you are well
Playlist to watch all videos on Learncommunolizer
• Maths Olympiad
And
• Maths
Subscribe: / @learncommunolizer

[@mantupramanik023]

Please short tricks ,this solution very long

[@ЛюдмилаЦыпышева-р4ц]

Умножить числитель и знаменатель дроби на 2, в знаменателе будет формула квадрат разности корня из 5 и корня из трех. А дальше только упростить! 😊

[@dennisdejong6540]

How did you see that the "a" and "b" would turn out to be 24 and 40?
Any clues I missed before hand?

[@paulortega5317]

let x = the answer. u = x/4. Then u^2 = 4+sqrt(15) and 1/u^2 = 4-sqrt(15). u^2+1/u^2 = 8 and then u+1/u=sqrt(10). u^2+1=u*sqrt(10). 5+sqrt(15)=u*sqrt(10). u=(5+sqrt(15))/sqrt(10). u=sqrt(2)*(sqrt(5) + sqrt(3))/2. x = 4u = 2*sqrt(2)*(sqrt(5) + sqrt(3)).

[@muratyasaryldz8168]

Çok güzel bir paylaşım.Muzik ve matematik öyle muhteşem bilim ki konuşmaları anlamasam da ne yaptığınızı anliyorum.Cok teşekkürler

[@kenrutherford7607]

splendid!!!!

[@betto63mx92]

Para no obtener un resultado como el que esperaba, propongo esta alternativa mas directa y con un resultado como el que tampoco me convence .
.
A partir de
Sq(64 + 16 sq15)
Sq( 16 ( 4 + sq15 ))
4sq( 4 + sq15)

[@АндрейПергаев-з4н]

Умножить на 2
Sqrt (32/(8-2sqrt 15))
Таким образом
32=2*4^2
8-2sqrt 15=(sqrt 5-sqrt 3)^2
Извлечение квадратного корня
4 *sqr2 /(sqrt 5-sqrt 3)
Избавиться от иррациональности в знаменателе
4 sqrt 2*(sqrt 5+sqrt3) /2=2 sqrt 10+2sqrt6
2 минуты, а не 8 как на видео

[@רובימהאנדרואיד]

Thank u ❤

[@learncommunolizer]

You're welcome 😊

[@reinhardtristaneugen9113]

also ich habe da 11 vor dem Komma, aber weil das natürlich zum Quadrat 121 ergibt, musste ich weiterrechnen, und kam auf 11,09.
Wie ich darauf kam?
Ich zog die Wurzel von 15 im Kopf, was mich zu 3,87 führte und subtrahierte und das brachte mich zu 13 / 100, wobei man ja dividiert, indem man mit dem Kehrwert multipliziert, sodass ich 1600 durch 13 hatte und das führt zu 123 und eben zu 11.09, so man die Wurzel zieht.
Le p'tit Daniel

[@gnanadesikansenthilnathan6750]

Clear. Splendid and excellent.

[@learncommunolizer]

Thanks. Your welcome

[@key_board_x]

= √[16 / (4 - √15)]
= √[16.(4 + √15) / {(4 - √15).(4 + √15)} ]
= √[16.(4 + √15) / {16 - 15} ]
= √[16.(4 + √15)]
= 4√(4 + √15) → you need to find a number x sush as x² = 4 + √15
Suppose that: x = √a + √b
x = √a + √b
x² = (√a + √b)²
x² = (√a)² + 2.(√a).(√b) + (√b)²
x² = a + 2.√(ab) + b
x² = (a + b) + 2.√(ab) → by identification to (4 + √15)
a + b = 4
2.√(ab) = √15
√(ab) = (1/2).√15
√(ab) = √[(1/4) * 15]
ab = (1/4) * 15
ab = 15/4
Resume
a + b = 4 ← this is the sum S
ab = 15/4 ← this is the product P
a & b are the solution of the equation:
x² - Sx + P = 0
x² - 4x + (15/4) = 0
Δ = (- 4)² - [4 * (15/4)] = 16 - 15 = 1
x = (4 ± 1)/2
x = 5/2 ← this is a
x = 3/2 ← this is b
We can see that:
[ √(3/2) + √(5/2) ]² = (3/2) + 2√[(3/2) * (5/2)] + (5/2)
[ √(3/2) + √(5/2) ]² = (8/2) + 2√(15/4)
[ √(3/2) + √(5/2) ]² = 4 + √15
Restart:
= 4√(4 + √15)
= 4√[ √(3/2) + √(5/2) ]²
= 4.[√(3/2) + √(5/2)]
= 4√(3/2) + 4√(5/2)
= √(48/2) + √(80/2)
= √24 + √40
= 2√6 + 2√10
= 2.(√6 + √10)

[@mathshindustani6216]

There is easier way to solve this bro
U made it lengthy
But nice try

[@lifewatery7472]

√[16/(4-√15)]
=√[32/(8-2√15)]
=√{32/[(√5)²-2√5•√3+(√3)²]}
=√[32/(√5-√3)²]
=4√2/(√5-√3)
=4√2(√5+√3)/[(√5-√3)•(√5+√3)]
=4√2(√5+√3)/2
=2√2(√5+√3)

[@lifewatery7472]

√[16/(4-√15)]
=4√[2/(8-2√15)]
=4√2/√{[(√5)²-2√5•√3+(√3)²]}
=4√2/√(√5-√3)²
=4√2/(√5-√3)
=4√2(√5+√3)/[(√5-√3)•(√5+√3)]
=4√2(√5+√3)/2
=2√2(√5+√3)

[@الأستاذتيسيرنصار]

الجاواب النهائي مش مختصر نهائيا

[@arturchirki]

Бессмысленная задача, и никакой красоты в решении и ответа.Задача смотрится проще, чем ответ.

[@mauriziograndi1750]

You right here we see taking pleasure in writing plenty of small steps.
I believe the shorter is the smartest.

[@aeroeng22]

that's funny, Harris begging for your hard earned cash at the beginning of this video, in an ad. I wouldn't show her the restroom if her hair was on fire.

[@doctobi9437]

Notnonly in your last Line but for example: SquareRoot of 4 could also be -2...so you lost some solutions...sorry

[@dashinglover9629]

Square root is always positive

[@doctobi9437]

thank you. I went wrong because x^2=4 has two solutions -2 and +2

[@shehzar_hn2680]

​@@doctobi9437There is difference between x2 =4 has to solution...Here we remove power
But when √4 only positive value comes out ...With mod

[@ИльяПросветов-ю9о]

Как же бесят переписывания по 100 раз одно и тоже

[@OscarTejada2014]

7 minutes of my life just to see it wasn’t solved at all… go out and have a social life

[@krzysztofzajac4446]

what does your social life consist of? watching films on youtube? go out and have a real social life...

[@anonymousperson4466]

​@@krzysztofzajac4446atleast not solving a square root to get another

[@ARTMUSICGOL]

En Perú, ese ejercicio se hace en 1 minuto y en 4 o 5 líneas ... Hicieron un procedimiento demasiado largo y tedioso.