Multiplying Radicals Worksheet
Grade 10 Math worksheet covering multiplication of radical expressions, including simplifying and rationalizing denominators.
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Multiplying Radicals
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Simplify each radical expression by multiplying and then reducing to the simplest form. Rationalize all denominators where necessary.
1. Multiply and simplify: \(\sqrt{3} \cdot \sqrt{12}\)
2. Multiply and simplify: \(2\sqrt{5} \cdot 3\sqrt{10}\)
3. Multiply and simplify: \((4\sqrt{2})(5\sqrt{6})\)
4. To rationalize the denominator of \(\frac{1}{\sqrt{7}}\), you multiply by \(\frac{\sqrt{7}}{\sqrt{7}}\) to get .
5. The product of \((2 + \sqrt{3})(2 - \sqrt{3})\) is .
6. Which of the following is equivalent to \(\sqrt{8} \cdot \sqrt{2}\)?
\(\sqrt{10}\)
4
\(2\sqrt{4}\)
16
7. Multiply and simplify: \(\sqrt{x}(\sqrt{x} + \sqrt{y})\)
8. Multiply and simplify: \((3\sqrt{2} - 1)(2\sqrt{2} + 5)\)
9. \(\sqrt{50} = 5\sqrt{2}\)
True
False