Rationalizing Radicals Worksheet
A Grade 10 math worksheet focusing on rationalizing single-term and binomial denominators with radicals.
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Rationalizing Radicals
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Read each question carefully and rationalize the denominator where necessary. Show all your work.
Rationalize the denominator for each expression.
1. $$\frac{3}{\sqrt{5}}$$
2. $$\frac{10}{\sqrt{2}}$$
3. $$\frac{6}{2\sqrt{3}}$$
Rationalize the denominator for each expression involving binomials.
4. $$\frac{1}{2 + \sqrt{3}}$$
5. $$\frac{5}{\sqrt{7} - \sqrt{2}}$$
6. Which of the following is the rationalized form of $$\frac{4}{\sqrt{8}}$$?
$$\frac{\sqrt{2}}{2}$$
$$\sqrt{2}$$
$$2\sqrt{2}$$
$$\frac{4\sqrt{8}}{8}$$
Complete the statements below.
7. To rationalize a denominator with a single square root, multiply both the numerator and the denominator by the .
8. The conjugate of $$(a + \sqrt{b})$$ is .
9. Rationalize the denominator of the expression: $$\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$$