What is the following quotient? the fraction with numerator 3 square root of 8 and denominator 4 square root of 6

Simplify the numerator: 3√8 = 6√2. Then (6√2)/(4√6) = (3/2)√(2/6) = (3/2)√(1/3). Since √(1/3) = 1/√3, this becomes 3/(2√3) = √3/2 after rationalizing the denominator. The quotient is √3/2, choice B.

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