Final answer:
To simplify and divide √5 / √3, we express the square roots in exponential form, subtract the exponents, and rationalize the denominator resulting in the answer √15/3, which corresponds to option (B).
Step-by-step explanation:
To simplify and divide the given radical expression, √5 / √3, we'll use the rule of division of exponentials and properties of square roots. We start by expressing the square roots in exponential form:
√5 can be written as 51/2, and √3 can be written as 31/2. To divide these, we subtract the exponents of the exponential terms according to the division rule. The expression then becomes:
51/2 / 31/2 = (5/3)1/2
However, we cannot leave the expression with a radical in the denominator. To rationalize the denominator, we multiply both the numerator and the denominator by √3, which gives us:
(51/2 * 31/2) / (31/2 * 31/2) = √15 / 3
Therefore, the correct answer is (B) √15/3.