​ If a, b, c are positive real numbers, then √ a^(-1)b x √ b^(-1)c x √c^(-1)a is equal to ​

Question

If a, b, c are positive real numbers, then \(\sqrt{a^{-1}{b}}\times\)\(\sqrt{b^{-1}{c}}\times\)\(\sqrt{c^{-1}{a}}\) is equal to

A. 1 

B. abc 

C. \(\sqrt{abc}\)

D.\(\frac{1}{abc}\)

Answer 1

(b/a)^1/2 × (c/b)^1/2 × (a/c)^1/2

= (b/a × c/b × a/c)^1/2

= 1