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Question : 79 of 86

Marks: +1, -0

a, b, c

\sqrt{a^{-1} b}, \sqrt{b^{-1} c}, \sqrt{c^{-1} a}

Solution:

Concept:

Product of square roots simplifies by multiplying radicands inside a single square root.

Explanation:

Step 1: Write the product:

\sqrt{a^{-1}b} \cdot \sqrt{b^{-1}c} \cdot \sqrt{c^{-1}a}

Step 2: Combine under one square root:

\sqrt{(a^{-1}b)(b^{-1}c)(c^{-1}a)}

Step 3: Simplify inside:

a^{-1} \cdot b \cdot b^{-1} \cdot c \cdot c^{-1} \cdot a = (a^{-1}a)(b b^{-1})(c c^{-1}) = 1\cdot 1\cdot 1 = 1

Step 4: So the product equals

\sqrt{1} = 1

Answer:

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