To simplify the given expression, we can first rewrite it as a fraction.
sqrt(9) ÷ sqrt(3) ⇔ sqrt(9)/sqrt(3)
Now, we can rationalize the denominator of the quotient.
To do that, we will multiply the numerator and denominator by a factor that will make the denominator a perfect square inside the square root. We will do this using the fact that we can multiply the radicands of radicals if they have the same index.
If sqrt(a) and sqrt(b) are real numbers,
then sqrt(a)* sqrt(b)= sqrt(ab).
Let's start by finding the exponents necessary to create perfect squares in the denominator. Our goal is to have two of each factor.