Radical Remix Guided Notes
Radical Remix
Guided Notes: Adding & Multiplying
STUDENT ID TRACK #
NAME:
DATE:
Volume 1: Numerical Only
Track 01: The "Like Terms" Rule
Just like combining like terms in algebra (like \(3x + 2x = 5x\)), we can only add or subtract radicals if they are "LIKE RADICALS".
What makes them "Like"?
- Same index (the root number)
- Same radicand (the number inside)
\(a\sqrt{x} \pm b\sqrt{x} = (a \pm b)\sqrt{x}\)
Example A: Adding Like Radicals
\(7\sqrt{5} + 4\sqrt{5} =\)
Example B: Subtracting Like Radicals
\(10\sqrt{2} - 3\sqrt{2} =\)
Track 02: Amplifying (Multiplying)
To multiply radicals, we use the Product Property. You don't need like terms to multiply!
\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)
(Note: Radicands must be non-negative)
The Golden Rule: "Inside with Inside, Outside with Outside"
\(a\sqrt{x} \cdot b\sqrt{y} = (a \cdot b)\sqrt{x \cdot y}\)
Example C: Basic Multiplication
\(3\sqrt{2} \cdot 4\sqrt{7} =\)
Example D: Simplify Result
\(\sqrt{2} \cdot \sqrt{8} =\)
The Studio Session Checklist
- ONLY combine radicals with matching radicands.
- Add/Subtract the coefficients, keep the radical same.
- Multiply coefficients together and radicands together.
- ALWAYS check if your final answer can be simplified!
Radical Remix Extended Worksheet
Radical Remix
Extended Play: Studio Practice
NAME:
DATE:
Track 01: The "Like Terms" Jam
Combine the matching radicands!
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\(4\sqrt{3} + 9\sqrt{3}\)
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\(15\sqrt{6} - 7\sqrt{6}\)
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\(\sqrt{10} + 5\sqrt{10} + 2\sqrt{10}\)
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\(8\sqrt{2} - \sqrt{2}\)
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\(12\sqrt{5} + 3\sqrt{5} - 6\sqrt{5}\)
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\(2\sqrt{11} - 9\sqrt{11}\)
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\(5\sqrt{7} - 5\sqrt{7}\)
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\(3\sqrt{13} + \sqrt{13} - 4\sqrt{13}\)
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\(6\sqrt{3} + 2\sqrt{3}\)
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\(11\sqrt{2} - 4\sqrt{2}\)
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\(7\sqrt{15} + 3\sqrt{15}\)
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\(20\sqrt{7} - 12\sqrt{7}\)
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\(\sqrt{6} + \sqrt{6} + \sqrt{6}\)
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\(9\sqrt{10} - 10\sqrt{10}\)
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\(8\sqrt{14} + 2\sqrt{14}\)
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\(17\sqrt{3} - 6\sqrt{3} + \sqrt{3}\)
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\(4\sqrt{19} - 4\sqrt{19}\)
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\(2\sqrt{22} + 3\sqrt{22} + 5\sqrt{22}\)
Track 02: Amplified Multiplication
Multiply coefficients, then multiply radicands!
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\(\sqrt{2} \cdot \sqrt{5}\)
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\(3\sqrt{3} \cdot 2\sqrt{5}\)
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\(\sqrt{6} \cdot \sqrt{6}\)
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\(4\sqrt{2} \cdot 5\sqrt{3}\)
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\(2\sqrt{10} \cdot \sqrt{5}\)
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\(\sqrt{8} \cdot \sqrt{2}\)
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\(3\sqrt{15} \cdot 2\sqrt{3}\)
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\(\sqrt{7} \cdot \sqrt{3}\)
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\(5\sqrt{2} \cdot 2\sqrt{2}\)
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\(4\sqrt{5} \cdot 3\sqrt{2}\)
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\(\sqrt{11} \cdot \sqrt{11}\)
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\(2\sqrt{6} \cdot 3\sqrt{6}\)
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\(10\sqrt{2} \cdot \sqrt{10}\)
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\(\sqrt{3} \cdot \sqrt{12}\)
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\(4\sqrt{7} \cdot 2\sqrt{7}\)
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\(3\sqrt{2} \cdot 6\sqrt{8}\)
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\(5\sqrt{6} \cdot 2\sqrt{3}\)
Radical Remix Answer Key Extended
Master Tracks
Teacher Answer Key: Extended Edition
Full Set (35 Tracks)
Track 01: Like Terms Jam
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\(13\sqrt{3}\)
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\(8\sqrt{6}\)
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\(8\sqrt{10}\)
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\(7\sqrt{2}\)
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\(9\sqrt{5}\)
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\(-7\sqrt{11}\)
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\(0\)
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\(0\)
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\(8\sqrt{3}\)
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\(7\sqrt{2}\)
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\(10\sqrt{15}\)
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\(8\sqrt{7}\)
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\(3\sqrt{6}\)
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\(-\sqrt{10}\)
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\(10\sqrt{14}\)
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\(12\sqrt{3}\)
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\(0\)
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\(10\sqrt{22}\)
Track 02: Amplified Multiplying
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\(\sqrt{10}\)
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\(6\sqrt{15}\)
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\(6\)
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\(20\sqrt{6}\)
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\(10\sqrt{2}\)
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\(4\)
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\(18\sqrt{5}\)
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\(\sqrt{21}\)
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\(20\)
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\(12\sqrt{10}\)
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\(11\)
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\(36\)
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\(20\sqrt{5}\)
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\(6\)
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\(56\)
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\(72\)
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\(30\sqrt{2}\)
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