Rationalizing Radicals Worksheet

Rationalizing Radicals

Read each question carefully and rationalize the denominator in each expression. Simplify your answers completely.

1. Rationalize the denominator: \(\frac{3}{\sqrt{5}}\)

2. Simplify and rationalize the denominator: \(\frac{6}{\sqrt{12}}\)

3. Rationalize the denominator: \(\frac{1}{2 + \sqrt{3}}\)

4. Rationalize the denominator: \(\frac{\sqrt{2}}{5 - \sqrt{2}}\)

5. To rationalize a denominator of the form \(a + \sqrt{b}\), you multiply the numerator and denominator by its  .

6. The product of \((X - Y)(X + Y)\) is \(X^2 - Y^2\), which is known as the   of squares.

7. Rationalizing the denominator means removing any radical expressions from the numerator.

8. Rationalize the denominator: \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)