Operations with Radicals
This worksheet focuses on simplifying, adding, subtracting, multiplying, and dividing radical expressions for Grade 9 students.
Includes
Standards
Operations with Radicals
Name:
Date:
Score:
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: \(\frac{\sqrt{48}}{\sqrt{6}}\)
Related Worksheets
Grade 9 Proportional Equations Worksheet
This worksheet focuses on understanding and solving proportional equations, including direct and inverse proportions, for Grade 9 students.
Zero Product Property Worksheet
Practice solving quadratic equations using the Zero Product Property for Grade 9 algebra.
Solving Three-Step Equations
This worksheet provides practice for grade 9 students in solving linear equations that require three steps.
Elimination Method Worksheet
Practice solving systems of linear equations using the elimination method for Grade 9 students.
Introduction to Imaginary Numbers
Explore the basics of imaginary numbers, their definition, and simple operations. This worksheet is designed for Grade 9 students.
Synthetic Substitution Practice Worksheet
Practice worksheet for synthetic substitution, suitable for grade 9 algebra students.
Grade 9 Linear Systems Worksheet
This worksheet covers solving linear systems using various methods, including graphing, substitution, and elimination, suitable for Grade 9 algebra students.
Identifying Unlike Terms Worksheet
A Grade 9 math worksheet focusing on identifying and understanding unlike terms in algebraic expressions.