If a, b, c are real numbers, then the value of \sqrt{a^{-1}b}.\sqrt{b^{-1}c}.\sqrt{c^{-1}a} is:

Surds and Indices Practice Test 1

Question : 36 of 40

Marks: +1, -0

If a, b, c are real numbers, then the value of

√{a^{-1}b}.√{b^{-1}c}.√{c^{-1}a}

is:

Solution:

√{a^{-1}b}.√{b^{-1}c}.√{c^{-1}a}

= {a^{-1/2}.b^{1/2}}.b^{-1/2}.c^{1/2}. {c^{-1/2}.a^{1/2}}

=a^{1/2-1/2}.c^{1/2-1/2}.b^{1/2-1/2}

=a^0 .b^0 .c^0=1

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