Final answer:
To simplify √3/ 2√5, we rationalize the denominator by multiplying both numerator and denominator by √5, resulting in √15/10 as the simplest form.
Step-by-step explanation:
To find the quotient of √3/ 2√5 in simplest terms, we need to simplify the expression by rationalizing the denominator.
Starting with the given expression, √3/ 2√5, we multiply the numerator and the denominator by √5 to eliminate the radical from the denominator.
√3 × √5 / (2√5 × √5) results in (√3 × √5) / 10, because √5² is 5. Now we can use the property of square roots that states √(a) × √(b) = √(ab) to further simplify the expression.
Therefore, we have √(3×5) / 10, which simplifies to √15 / 10. This can further be simplified to √15 / 10, which is the simplest form of the original expression.