Divide 9x^2 square root by square root 18y^2

To start, first write out the expression, which would be √9x^2/√18y^2. Then, you simplify the radicals in the numerator and the denominator. Since 9 has a square root of 3 and x^2 has a square root of x, √9x^2 would simplify to 3x. Then, since 18 cannot be square rooted, you look for any ways to simplify it. Since √18 can be divided into √9 and √2, you find that it can be simplified into 3√2 since √9 simplifies to 3, so you leave the 3 outside while you keep the 2 inside. Now, you look at √y^2. This easily simplifies to y. Now your expression looks like this: 3x/3y √2. Then, since they both have a common factor of 3, you divide 3 from both sides. Now your expression looks like this: x/y √2. Since you have to rationalize the denominator (meaning no radicals in the denominator), you have to multiply your expression by √2/√2 in order to keep the expression equivalent and rationalized. Your final answer should be x √2/2y