Rationalizing Denominators

What does it mean to rationalize the denominator?

What is the first step in rationalizing a denominator that contains a square root?

Rationalize the denominator: $$\frac{\sqrt{5x^4}}{\sqrt{2x^2y^3}}$$

Rationalize the denominator: $$\frac{\sqrt{40x^5y^3z^7}}{\sqrt{3x^3yz}}$$

Rationalize the denominator: $$\frac{15\sqrt{60x^5}}{3\sqrt{12x}}$$

Rationalize the denominator: $$\frac{3\sqrt{11x^3y}}{-2\sqrt{12x^4y}}$$

What is the result of multiplying a radical by itself?

How do you simplify a fraction with a radical in the denominator?

What is the simplified form of $$\frac{2x^3\sqrt{30}}{y^3\sqrt{3x}}$$ ?

What is the purpose of rationalizing the denominator in mathematics?