Operations with Radicals
This worksheet focuses on simplifying, adding, subtracting, multiplying, and dividing radical expressions for Grade 9 students.
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Standards
Operations with Radicals
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Read each question carefully and perform the indicated operations with radical expressions. Simplify all answers completely.
1. Which of the following is equivalent to \(\sqrt{72}\)?
\(6\sqrt{2}\)
\(2\sqrt{6}\)
\(3\sqrt{8}\)
\(8\sqrt{9}\)
Simplify the following radical expressions:
2. \(\sqrt{125} = \)
3. \(\sqrt{98x^3} = \)
4. Simplify the expression: \(3\sqrt{5} + 7\sqrt{5} - \sqrt{5}\)
5. Simplify the expression: \(\sqrt{20} + \sqrt{45}\)
Match each multiplication problem with its simplified answer.
6. \(\sqrt{3} \cdot \sqrt{12}\)
a. \(2\sqrt{10}\)
7. \(2\sqrt{5} \cdot \sqrt{2}\)
b. \(6\)
8. \((\sqrt{6})^2\)
c. \(6\sqrt{2}\)
9. Rationalize the denominator and simplify: \(\frac{1}{\sqrt{3}}\)
10. Simplify the expression: \(\frac{\sqrt{48}}{\sqrt{6}}\)