Can You Simplify Another Radical?

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4 окт 2024

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Комментарии : 16

@jamesmarshall7756 День назад

Great as usual !

@SyberMath День назад

Glad you think so!

@jakeaustria5445 День назад

Thank You ❤

@SyberMath День назад

You're welcome 😊

@-wx-78- День назад

Apply nested radical formula: √(x±√y) = √[½(x+D)] ± √[½(x−D)], where D = √(x²−y). D = √[a²−(a²−9)] = √9 = 3, √[a−√(a²−9)] = √[½(a+3)] − √[½(a−3)]. It works every time x²−y is a perfect square: √[3−√(9−a²)] = √[½(3+|a|)] − √[½(3−|a|)], since D = √[3²−(9−a²)] = |a|.

@pjb.1775 День назад

I CANT. WE CANT. STOP ASKING. I CANT DENEST A RADICAL. THATS WHY THEYRE CALLED RADICALS

@petrileskinen2988 День назад

Interesting, instead of a constant 9 this could be applied for a more general case sqrt(a-sqrt(a^2 - b^2)) = sqrt((a+b)/2) - sqrt((a-b)/2)

@Fjfurufjdfjd День назад

Η σχεση γραφεται: [α-2[(α+3)(α-3)/4]^(1/2)]^(1/2)=[[(α+3)/2 +(α-3)/2-2[(α+3)/2 ×(α-3)/2]^(1/2)=[(α+3)/2]^1/2-[(α-3)/2]^1/2

@scottleung9587 День назад

Nice!

@SyberMath День назад

Thanks!

@alipourzand6499 День назад

Simon would prefere the 3rd method! ☺

@dan-florinchereches4892 День назад

If √(a-√b)=√c-√d then a=c+d b=4cd Then a=c+b/4c 4c^2-4ac+b=0 so c = (4a+√(16a^2-16b))/8= (a+√(a^2-b))/2 and d =(a-√(a^2-b))/2 This makes the radical in the problem: √(a-√(a^2-9))=1/√2( √(a+√(a^2-a^2+9))-√(a-√(a^2-A^2+9))= 1/√2(√(a+3)-√(a-3))

@Don-Ensley 23 часа назад

problem simplify √[a-√(a²-9)] Let this be the difference between two square roots. Pick difference instead of sum because of the sign on the nested root being negative. √[a-√(a²-9)] = √x-√y square both sides a-√(a²-9) = x+y-2√(xy) equate coefficients of like terms to get a system of equations for x and y in terms of a: a = x+y √(a²-9) = 2√(xy) a²-9 = 4xy y = a-x a²-9 = 4x(a-x) = 4xa -4x² 4x²-4ax +a²-9 = 0 x = ½ (a+3), ½ (a-3) y = ½ (a-3), ½ (a+3) √[a-√(a²-9)] = √x -√y = √[½ (a+3)] -√[½ (a-3)] or √[a-√(a²-9)] = √x -√y = √[½ (a-3)] -√[½ (a+3)] These are opposites so √[a-√(a²-9)] = ± { √[½ (a+3)] -√[½ (a-3)] } answer √[a-√(a²-9)] = ± { √[½ (a+3)] -√[½ (a-3)] }