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

We have to find the value of when a, b, c are positive real numbers.

So,

Taking square root as common we get

$$\begin{gathered} \sqrt{a^{-1}b}\times \sqrt{b^{-1}c}\times \sqrt{c^{-1}a}=\sqrt{\frac{b}{a}\times \frac{c}{b}\times \frac{a}{c}} \\ \sqrt{a^{-1}b}\times \sqrt{b^{-1}c}\times \sqrt{c^{-1}a}=1 \end{gathered}$$

Hence the correct alternative is .