The correct option is C 1 √(x^ 1y).√(y^ 1z).√(z^ 1x) ⇒ #160; √(yx).√(zy).√(xz) ⇒ #160; √(yx×zy×xz) ⇒ #160; 1 ∴ ...

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Irrational Numbers on the Number Line

√x-1y.√y-1z.√...

Question

$\sqrt{x^{- 1} y} . \sqrt{y^{- 1} z} . \sqrt{z^{- 1} x} =$

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Solution

The correct option is C 1
$\sqrt{x^{- 1} y} . \sqrt{y^{- 1} z} . \sqrt{z^{- 1} x}$

$\Rightarrow$ $\sqrt{\frac{y}{x}} . \sqrt{\frac{z}{y}} . \sqrt{\frac{x}{z}}$

$\Rightarrow$ $\sqrt{\frac{y}{x} \times \frac{z}{y} \times \frac{x}{z}}$

$\Rightarrow$ $1$

$∴$ $\sqrt{x^{- 1} y} . \sqrt{y^{- 1} z} . \sqrt{z^{- 1} x} = 1$

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