Unit 1 • Lessons 5–7 (Radicals & Mixed Radicals)
Simplifying radicals • Entire ↔ mixed radicals • Add/Subtract • Multiply/Divide • Applications
Simplify
Entire ↔ Mixed
Combine Like Radicals
Multiply/Divide
Whiteboard Work
Practice Set
Each question allows 2 attempts. Use the built-in whiteboard to show your work, then click Reveal Solution if needed.
1) Simplify
Write \(\sqrt{98}\) in simplest radical form.
\(98=49\cdot 2\Rightarrow \sqrt{98}=7\sqrt{2}\) (simplest form).
2) Entire Radical
Write \(3\sqrt{8}\) as an entire radical.
\(3\sqrt{8}=\sqrt{3^2\cdot 8}=\sqrt{72}\).
3) Mixed Radical
Write \(\sqrt{288}\) as a mixed radical in simplest form.
\(288=144\cdot 2\Rightarrow \sqrt{288}=12\sqrt{2}\).
4) Add Radicals
Simplify \(2\sqrt{18}+5\sqrt{8}\).
\(2\sqrt{18}=2\cdot 3\sqrt{2}=6\sqrt{2},\;5\sqrt{8}=5\cdot 2\sqrt{2}=10\sqrt{2}\Rightarrow 16\sqrt{2}.\)
5) Combine Radicals
Simplify \(3\sqrt{50}-2\sqrt{8}+\sqrt{32}\).
\(3\sqrt{50}=3\cdot 5\sqrt{2}=15\sqrt{2}\), \(\;2\sqrt{8}=4\sqrt{2}\), \(\;\sqrt{32}=4\sqrt{2}\).
\(15\sqrt{2}-4\sqrt{2}+4\sqrt{2}=15\sqrt{2}.\)
6) Multiply Radicals
Compute \((3\sqrt{12})(2\sqrt{27})\).
\(3\sqrt{12}\cdot 2\sqrt{27}=6\sqrt{324}=6\cdot 18=108.\)
7) Divide Radicals
Simplify \(\dfrac{\sqrt{45}}{3\sqrt{5}}\).
\(\sqrt{45}=3\sqrt{5}\Rightarrow \dfrac{\sqrt{45}}{3\sqrt{5}}=\dfrac{3\sqrt{5}}{3\sqrt{5}}=1.\)
8) Application
A square has area \(98\text{ cm}^2\). Give the exact side length in simplest radical form.
Side \(=\sqrt{98}=7\sqrt{2}\text{ cm}\).
Progress
Score: 0/8