Adding, Subtracting, & Multiplying Radicals
Algebra 1 - Unit 3, Day 2
Today's Objective
Do Now: Review & Connect
Simplify each expression.
\( 3x + 5x = ? \)
\( 10y - 4y = ? \)
\( \sqrt{18} = ? \)
The Big Idea: Like Radicals
You can only add or subtract radicals that have the exact same root and radicand.
Think of them like "like terms":
\(3x + 5x = 8x\)
\(3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2}\)
Sometimes you must simplify first to find like radicals!
Practice: Adding & Subtracting
I Do
\(3\sqrt{5} + 6\sqrt{5}\)
\((3+6)\sqrt{5}\)
\(9\sqrt{5}\)
We Do
\(10\sqrt{7} - 2\sqrt{7}\)
\((10-2)\sqrt{7}\)
\(8\sqrt{7}\)
You Do
\(-\sqrt{10} + 5\sqrt{10}\)
\((-1+5)\sqrt{10}\)
\(4\sqrt{10}\)
I Do: \(3\sqrt{5} + 6\sqrt{5}\) = 9\(\sqrt{5}\)
We Do: \(10\sqrt{7} - 2\sqrt{7}\) =
You Do: \(-\sqrt{10} + 5\sqrt{10}\) =
Practice: Simplify First!
I Do
\(\sqrt{12} + \sqrt{75}\)
\(\sqrt{4 \cdot 3} + \sqrt{25 \cdot 3}\)
\(2\sqrt{3} + 5\sqrt{3}\)
\(7\sqrt{3}\)
We Do
\(\sqrt{50} - \sqrt{8}\)
\(\sqrt{25 \cdot 2} - \sqrt{4 \cdot 2}\)
\(5\sqrt{2} - 2\sqrt{2}\)
\(3\sqrt{2}\)
I Do: \(\sqrt{12} + \sqrt{75}\) = 7\(\sqrt{3}\)
We Do: \(\sqrt{50} - \sqrt{8}\) =
Multiplying Radicals
To multiply radicals, multiply the coefficients together and the radicands together.
Always simplify the result!
Practice: Multiplying
I Do
\(\sqrt{6} \cdot \sqrt{3}\)
\(\sqrt{18}\)
\(\sqrt{9 \cdot 2}\)
\(3\sqrt{2}\)
We Do
\(2\sqrt{5} \cdot 3\sqrt{10}\)
\((2 \cdot 3)\sqrt{5 \cdot 10}\)
\(6\sqrt{50}\)
\(6\sqrt{25 \cdot 2} \rightarrow 6 \cdot 5\sqrt{2}\)
\(30\sqrt{2}\)
You Do
\(\sqrt{2}(\sqrt{8} + \sqrt{3})\)
\(\sqrt{16} + \sqrt{6}\)
\(4 + \sqrt{6}\)
I Do: \(\sqrt{6} \cdot \sqrt{3}\) = 3\(\sqrt{2}\)
We Do: \(2\sqrt{5} \cdot 3\sqrt{10}\) =
You Do: \(\sqrt{2}(\sqrt{8} + \sqrt{3})\) =
Independent Practice
Complete the following problems. Start with the green section!
Simplify:
1. \(8\sqrt{3} - 2\sqrt{3}\)
2. \(\sqrt{5} \cdot \sqrt{7}\)
Simplify:
3. \(4\sqrt{2} + \sqrt{32}\)
4. \(5\sqrt{3} \cdot \sqrt{6}\)
Simplify:
5. \(3\sqrt{8} + 2\sqrt{18} - \sqrt{50}\)
Independent Practice
1. \(8\sqrt{3} - 2\sqrt{3}\) =
2. \(\sqrt{5} \cdot \sqrt{7}\) =
3. \(4\sqrt{2} + \sqrt{32}\) =
4. \(5\sqrt{3} \cdot \sqrt{6}\) =
5. \(3\sqrt{8} + 2\sqrt{18} - \sqrt{50}\) =
Exit Ticket
Simplify the following expression completely:
\(3\sqrt{20} - \sqrt{5}\)
\(3\sqrt{4 \cdot 5} - \sqrt{5}\)
\(3 \cdot 2\sqrt{5} - \sqrt{5}\)
\(6\sqrt{5} - \sqrt{5}\)
Answer: \(5\sqrt{5}\)