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# 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
1 year 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 $$1 , -1 , \iota , -\iota$$ · 1 year ago

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

Option 1. First condition: xyz= -1 · 1 year ago

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

Option $$0!$$ · 1 year 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 · 1 year ago

Option 1 · 1 year ago

Explanation required · 1 year ago

(x^2n)^(1/2n)=|x| · 1 year ago

Nice · 1 year ago