Perform the indicated operations. Assume all variables represent positive real numbers.
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
- Appendix 1. Review of Real Numbers2h 24m
- Appendix 2. Linear Equations and Inequalities3h 42m
- OLD 9. Sequences, Induction, and Probability Coming soon
- 1. - OLD - Fundamental Concepts of Algebra Coming soon
- 2. - OLD - Equations and Inequalities Coming soon
- OLD 4. Rational Functions Coming soon
- OLD 2. Functions & Graphs Coming soon
- OLD 6. Exponential and Logarithmic Functions Coming soon
- OLD 7. Systems of Equations and Inequalities Coming soon
- OLD 8. Matrices and Determinants Coming soon
- OLD 9. Conic Sections Coming soon
0. Review of Algebra
Simplifying Radical Expressions
Multiple Choice
Simplify the radical.
180
A
65
B
35
C
320
D
245
0 Comments
Verified step by step guidance1
Identify the expression to simplify: \( 180\sqrt{180} \). The goal is to simplify the radical part.
Factor the number under the square root, \( 180 \), into its prime factors: \( 180 = 2^2 \times 3^2 \times 5 \).
Apply the property of square roots: \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). This allows us to separate the factors under the square root.
Simplify the square root by taking out pairs of prime factors: \( \sqrt{180} = \sqrt{2^2 \times 3^2 \times 5} = 2 \times 3 \times \sqrt{5} = 6\sqrt{5} \).
Multiply the simplified radical by the coefficient outside the square root: \( 180 \times 6\sqrt{5} = 1080\sqrt{5} \).
Related Videos
Related Practice
Textbook Question
7
views

