Which option is correct?

If \(xyz=-1\), then the value of \( \sqrt [ 4 ]{ \left( xyz \right)^4 } \) is

Option 1 : 1

Why?

Because

\[\Large{ \sqrt [ 4 ]{ \left( xyz \right)^4} =\sqrt [ 4 ]{ \left( -1 \right) ^{ 4 } } =\sqrt [ 4 ]{ 1 } =1}\]

Option 2 : -1

Why?

Because

\[\Large{\sqrt [ 4 ]{ \left( xyz \right) ^{ 4 } }=xyz=-1}\]

Option 3 : \(i\)

Why?

Because

\[\Large{\sqrt [ 4 ]{ \left( xyz \right) ^{ 4 } } =\quad \sqrt [ 4 ]{ \left( xyz \right) ^{ 3 } } \times \sqrt [ 4 ]{ xyz } =\sqrt { i } \times \sqrt { i } =i}\]

Explanation required

Note by Lakshya Sinha
2 years, 3 months ago

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1 vote

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Comments

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I think this one example may help you.
Ex. \((\sqrt{-1})^2 \neq \sqrt{(-1)^2}\)
LHS : \((\sqrt{-1})^2 = -1 \)
RHS : \(\sqrt{(-1)^2} = |-1| = 1 \)

I think all the options are correct. Given equation has 4 roots.i.e \(1 , -1 , \iota , -\iota\)

Akhil Bansal - 2 years, 3 months ago

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let x = xyz^4 so x will have roots ie i,-1,1,one more

Genius Literally - 2 years, 3 months ago

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Option 1. First condition: xyz= -1

Ma Pm - 2 years, 3 months ago

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Option 1, because the property that (a)^(mn)=a^m*a^n is only preserved for real numbers.

Aditya Agarwal - 2 years, 3 months ago

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Option \(0!\)

Hjalmar Orellana Soto - 2 years, 3 months ago

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option 1 guaranteed .option 2-no because the root sign stands for only positive values and option 3 -no because u cant do it for unreal numbers

Kaustubh Miglani - 2 years, 3 months ago

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Option 1

Deepak Kumar - 2 years, 3 months ago

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Explanation required

Lakshya Sinha - 2 years, 3 months ago

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(x^2n)^(1/2n)=|x|

Deepak Kumar - 2 years, 3 months ago

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@Deepak Kumar Nice

Lakshya Sinha - 2 years, 3 months ago

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Ya correct explanation.....its option 1

Ravi Dwivedi - 2 years, 3 months ago

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