Unit 2 • Lessons 1–3 (Operations on Radicals) — Quiz
Entire & mixed radicals • Adding & subtracting radicals • Multiplying radicals
Entire ↔ Mixed
Combine Like Radicals
Distribute & Conjugates
Practice Set
Each question allows 2 attempts. Use the whiteboard below each problem, then click Reveal Solution if needed.
1) Simplify to Mixed Radical
Simplify \(\sqrt{72}\).
\(72=36\cdot 2\Rightarrow \sqrt{72}=6\sqrt{2}.\)
2) Convert to Entire Radical
Write \(3\sqrt{50}\) as an entire radical.
\((3\sqrt{50})=\sqrt{3^2\cdot 50}=\sqrt{450}.\)
3) Add/Subtract Radicals
Simplify \(5\sqrt{18}-2\sqrt{8}+\sqrt{50}\).
\(\sqrt{18}=3\sqrt{2},\; \sqrt{8}=2\sqrt{2},\; \sqrt{50}=5\sqrt{2}\Rightarrow 15\sqrt{2}-4\sqrt{2}+5\sqrt{2}=16\sqrt{2}.\)
4) Combine Like Radicals
Simplify \(2\sqrt{12}+3\sqrt{27}-\sqrt{75}\).
\(2\cdot 2\sqrt{3}+3\cdot 3\sqrt{3}-5\sqrt{3}=4\sqrt{3}+9\sqrt{3}-5\sqrt{3}=8\sqrt{3}.\)
5) Multiply Radicals
Simplify \((\sqrt{12})(2\sqrt{18})\).
\(2\sqrt{12\cdot 18}=2\sqrt{216}=2\cdot 6\sqrt{6}=12\sqrt{6}.\)
6) Conjugates
Simplify \((\sqrt{5}+\sqrt{20})(\sqrt{5}-\sqrt{20})\).
\(\sqrt{20}=2\sqrt{5}\Rightarrow (a+b)(a-b)=a^2-b^2=5-(2\sqrt{5})^2=5-20=-15.\)
7) Multiply Radicals
Simplify \((3\sqrt{6})(2\sqrt{15})\).
\(3\cdot 2\sqrt{6\cdot 15}=6\sqrt{90}=6\cdot 3\sqrt{10}=18\sqrt{10}.\)
8) Expand & Simplify
Simplify \((\sqrt{8}+3\sqrt{2})^2\).
\(\sqrt{8}=2\sqrt{2}\Rightarrow (2\sqrt{2}+3\sqrt{2})^2=(5\sqrt{2})^2=25\cdot 2=50.\)
Progress
Score: 0/8