Algebra

sqrt(18xy) / sqrt(3x^2y)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Write as one fraction under radical

When dividing two square roots, we can combine them into one square root of a fraction. This makes simplifying much easier.
2

Simplify the fraction inside the radical

Divide the numbers: . Then cancel matching variables: and .
3

Write the simplified fraction inside radical

After canceling, we have 6 in the numerator and in the denominator. The terms cancelled out completely.
4

Rationalize the denominator

We can't leave a square root in the denominator. Multiply top and bottom by to clear it. This gives on the bottom.

Understanding this problem

Learning Insight

The rule works because square roots and fractions both follow the same multiplication properties. Rationalizing the denominator is a standard form requirement — it makes expressions easier to compare and use in further calculations.

Quick Tip

When you see variable division inside a radical, cancel variables first before worrying about the numbers. Fewer terms = fewer chances to make errors.

Common Mistake

Students often cancel as just instead of , flipping which variable ends up in the numerator vs. denominator.