# 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 Department 8
4 years ago

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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 $1 , -1 , \iota , -\iota$

- 4 years ago

Option $0!$

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

- 4 years ago

Option 1. First condition: xyz= -1

- 4 years ago

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

- 4 years ago

Option 1

- 4 years ago

Explanation required

- 4 years ago

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

- 4 years ago

Nice

- 4 years ago

Ya correct explanation.....its option 1

- 4 years ago

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

- 4 years ago