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

Options

• 1

• abc

• \[\sqrt{abc}\]

• \[\frac{1}{abc}\]

Answer 1

We have to find the value of  `sqrt(a^-1b)xx sqrt (b^-1c) xx sqrt(c^-1 a)` when a, b, c are positive real numbers.

So,

`sqrt(a^-1b)xx sqrt (b^-1c) xx sqrt(c^-1 a) =sqrt(1/a xxb)xx sqrt(1/b xx c) xx sqrt(1/c xx a)` 

`sqrt(b/a) xx sqrt (c/b) xx sqrt(a/c)`

Taking square root as common we get

\[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a} = \sqrt{\frac{b}{a} \times \frac{c}{b} \times \frac{a}{c}}\]

\[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a} = 1\]