Simplifying a Radical Expression in Two Ways

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(17+12sqrt(12))^{1/4}
#radicals #algebra
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[@andylee63]

Nice trick!

[@mcumer]

Another way: we can factorize 17+12sqrt(2) and therefore we but a^2+b^2=17 and 2ab= 12 sqrt(2).. if we put a^2=8 and b^2=9 , we obtain a=2 sqrt(2) and b=3.. the factorization is (3+2sqrt(2))^2.. simplifying the radical it becomes a square root.. factorizing 3+2sqrt(2) is easy ( 3=1+2 ..).. finally we can simplifly the square root

[@scottleung9587]

I used a method similar to your second.

[@SergeySvotin]

Also it's really simple sum, you can easily dissolve it as (3 + 2sqrt2)^2 which can be further dissolved as (1 + sqrt2)^4, all you have to do is to add +- when you apply sqrt on every step

[@mbmillermo]

Very cool. Another way to do it: Take the square root twice! Assume that √(17+12√2) has the form √a+√b. Then (√a+√b)² = a+b+2√(ab), so a+b=17 and ab=72. Thus a and b are 8 and 9 and we have √(17+12√2) = 3+2√2. Do it again and we get a+b=3 and ab=2, so a and b are 1 and 2 and our final solution is 1+√2.

[@forcelifeforce]

(√a + √b)² = a + b + 2√(ab) You need grouping symbols for the radicand because it is a product.

[@mbmillermo]

@@forcelifeforce - I'm glad you were able to understand me! You probably know the binomial formula. Next time I'll use parentheses.

[@mbmillermo]

@@forcelifeforce - Oh, I can edit it. I'll do that now.

[@alextang4688]

Simply two times for square root.😋😋😋😋😋😋

[@SergeySvotin]

9:35 and that brings us to -1-sqrt2, (1+sqrt2)i and -(1+sqrt2)i

[@tryingtomakeanamebelike7245]

Method on how to solve
Convert 12root(2) into 2root(72)
Check roots that multiply to 72 and add to 17
3 and 2root(2) work
However these factors can also be simplified to (root(2) + 1)^2
Meaning we have (root(2) + 1)^4
Answer is root(2) + 1
Edit: I know this thought process was basically method 2 but I did the problem before watching the video you gotta believe me

[@miguellumbombo9886]

Mas... no primeiro método, k=1/2 também verifica. Basta racionalizar o denominador e aplicar propriedade comutativa.

[@QuoraWorld]

Mind blowing sir😊😊👍👍👍👍🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹

[@teambellavsteamalice]

I used the second method in my head, very fast to factor 17&72 and then 3&2.

[@giuseppemalaguti435]

1+√2

[@Murlica]

simplifying brings me to 2 results: sqrt(2)+1 and -sqrt(2)-1

[@pmccarthy001]

Channel a+bi... Having trouble searching for that. Getting numerous results. Does anyone know what channel he's referrng to?

[@broytingaravsol]

very easy

[@SergeySvotin]

8:06 so you lost to mere numbers once again and missed one real and 2 complex solutions for this one -_-