ABC26GN1982 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $a, b, c$ are real numbers, then the value of $\sqrt{a^{-1} b} \cdot \sqrt{b^{-1} c} \cdot \sqrt{c^{-1} a}$ is
(a)$a b c$
(b)$\sqrt{a b c}$
(c)$\frac{1}{a b c}$
(d)1
Answer
Explanation
$\sqrt{a^{-1} b} \cdot \sqrt{b^{-1} c} \cdot \sqrt{c^{-1} a}=\left(a^{-1}\right)^{\frac{1}{2}} \cdot b^{\frac{1}{2}} \cdot\left(b^{-1}\right)^{\frac{1}{2}} \cdot c^{\frac{1}{2}} \cdot\left(c^{-1}\right)^{\frac{1}{2}} \cdot a^{\frac{1}{2}}$ $$\begin{aligned} & =\left(a^{-1} a\right)^{\frac{1}{2}} \cdot\left(b \cdot b^{-1}\right)^{\frac{1}{2}} \cdot\left(c \cdot c^{-1}\right)^{\frac{1}{2}} \\ & =(1)^{\frac{1}{2}} \cdot(1)^{\frac{1}{2}} \cdot(1)^{\frac{1}{2}}=(1 \times 1 \times 1)=1 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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