Section 2.3P: Practice
- Page ID
- 192808
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Practice Makes Progress
In the following exercises, simplify.
\(3\sqrt{5}+6\sqrt{5}\)
\(9\sqrt{7}−10\sqrt{7}\)
\(\sqrt{a}−4\sqrt{a}\)
\(8\sqrt{a}−2\sqrt{b}\)
\(8\sqrt{7}+2\sqrt{7}+3\sqrt{7}\)
\(5\sqrt{3ab}+\sqrt{3ab}−2\sqrt{3ab}\)
\(\sqrt{50}+4\sqrt{2}\)
\(\sqrt{80}−3\sqrt{5}\)
\(\sqrt{27}−\sqrt{75}\)
\(\sqrt{48}+\sqrt{27}\)
\(2\sqrt{50}−3\sqrt{72}\)
\(2\sqrt{12}+3\sqrt{48}\)
\(\frac{1}{6}\sqrt{27}−\frac{3}{8}\sqrt{48}\)
\(\frac{1}{4}\sqrt{98}−\frac{1}{3}\sqrt{128}\)
\(\sqrt{72a^5}−\sqrt{50a^5}\)
\(2\sqrt{50r^8}+4\sqrt{54r^8}\)
\(3\sqrt{20x^2}−4\sqrt{45x^2}+5x\sqrt{80}\)
\(\sqrt{175k^4}−\sqrt{63k^4}\)
\(9\sqrt{2}−8\sqrt{2}\)
\(8\sqrt{13}−4\sqrt{13}−3\sqrt{13}\)
\(\sqrt{80a^5}−\sqrt{45a^5}\)
\(21\sqrt{19}−2\sqrt{19}\)
\(\frac{5}{6}\sqrt{27}+\frac{5}{8}\sqrt{48}\)
\(\sqrt{75}−\sqrt{108}\)
\(4\sqrt{24x^2}−\sqrt{54x^2}+3x\sqrt{6}\)
Everyday Math
A decorator decides to use square tiles as an accent strip in the design of a new shower, but she wants to rotate the tiles to look like diamonds. She will use 9 large tiles, each measuring 8 inches on a side, and 8 small tiles, each measuring 2 inches on a side. Determine the width of the accent strip by simplifying the expression \(9(8\sqrt{2})+8(2\sqrt{2})\). (Round to the nearest tenth of an inch.)
Writing Exercises
Explain the difference between like radicals and unlike radicals. Ensure your answer is sensible for radicals that contain both numbers and variables.
Self Check
Use this checklist to evaluate your mastery of the objectives of this section.
If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is crucial to establish a strong foundation before proceeding. Who can you ask for help? Your classmates, tutors, and class instructor are good resources.
…no - I don’t get it! This is a warning sign, and you must not ignore it. You should get help right away, or you will quickly be overwhelmed. Meet with your instructor during their drop-in hours as soon as you can to discuss your situation. Together, you can devise a plan to get the help you need.