Multiplying Radicals Worksheet
Grade 11 Math worksheet on multiplying radicals, including simplifying expressions and rationalizing denominators.
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Multiplying Radicals
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Read each question carefully and show all your work. Simplify all radical expressions to their simplest form. Rationalize denominators where necessary.
1. Multiply and simplify the following radical expressions:
a) \( \sqrt{3} \cdot \sqrt{12} \)
b) \( (2\sqrt{5})(3\sqrt{10}) \)
c) \( \sqrt{6}(\sqrt{3} + \sqrt{2}) \)
2. Expand and simplify the following expressions:
a) \( (\sqrt{7} + 2)(\sqrt{7} - 2) \)
b) \( (3\sqrt{2} - 1)(2\sqrt{2} + 5) \)
3. Rationalize the denominator and simplify the expression:
a) \( \frac{1}{\sqrt{5}} \)
b) \( \frac{6}{3\sqrt{2}} \)
c) \( \frac{4}{2 + \sqrt{3}} \)
4. Which of the following is equivalent to \( \sqrt{18} \cdot \sqrt{2} \)?
\( \sqrt{36} \)
\( 6 \)
\( 3\sqrt{2} \)
\( 2\sqrt{3} \)
5. Determine if each statement is True or False.
a) \( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \) is always true for non-negative real numbers a and b.
True
False
b) \( (\sqrt{x} + \sqrt{y})^2 = x + y \) for all non-negative real numbers x and y.
True
False
6. Complete the following statements.
a) To rationalize a binomial denominator with a radical, multiply the numerator and denominator by its .
b) When multiplying radicals with the same index, we multiply the together and the together.