What is the quotient of √a and √b?

The correct answer is √a / √b, which represents the quotient of the square roots of a and b. This expression is based on the property of square roots that states the division of two square roots can be expressed as the square root of the quotient of the two numbers. Hence, √a / √b is equivalent to the ratio of the two square roots directly.

To further elaborate, when dividing square roots, you can rewrite this as follows:

√a / √b = √(a/b)

This shows that you can combine the square roots over the division of their respective values. Therefore, while the expression as it stands (√a / √b) is accurate in representing the direct quotient, it is also linked to another valid expression (√(a/b)), which may lead to confusion about equivalence.

The other expressions do not appropriately reflect the relationship of dividing square roots. For instance, a/√b does not conform to the properties of square roots, where the square root should be applied to the numerator and denominator if you are dividing their square roots. Similarly, √a / b would imply that b is not under the square root, which does not maintain the necessary mathematical structure for this operation.

Thus,