Simplifying Square & Cube Roots
Algebra 1 - Unit 3, Day 1
Today's Objective
Do Now: Find the Missing Number!
\( 3 \times 3 = ? \)
\( ? \times ? = 25 \) (use the same number)
\( 10 \times 10 = ? \)
\( ? \times ? = 81 \) (use the same number)
Brain Break: Perfect Roots
Perfect Squares
\(2^2 = 4\)
\(3^2 = 9\)
\(4^2 = 16\)
\(5^2 = 25\)
\(6^2 = 36\)
\(7^2 = 49\)
\(8^2 = 64\)
\(9^2 = 81\)
\(10^2 = 100\)
\(12^2 = 144\)
Perfect Cubes
\(2^3 = 8\)
\(3^3 = 27\)
\(4^3 = 64\)
\(5^3 = 125\)
The Big Idea
To simplify a radical, we "pull out" the largest perfect root factor from the radicand.
Practice: Square Roots
I Do
\(\sqrt{72}\)
\(\sqrt{36 \cdot 2}\)
\(\sqrt{36} \cdot \sqrt{2}\)
\(6\sqrt{2}\)
We Do
\(\sqrt{50}\)
\(\sqrt{25 \cdot 2}\)
\(\sqrt{25} \cdot \sqrt{2}\)
\(5\sqrt{2}\)
You Do
\(\sqrt{98}\)
\(\sqrt{49 \cdot 2}\)
\(\sqrt{49} \cdot \sqrt{2}\)
\(7\sqrt{2}\)
I Do: \(\sqrt{72}\) = 6\(\sqrt{2}\)
We Do: \(\sqrt{50}\) =
You Do: \(\sqrt{98}\) =
Practice: Cube Roots
I Do
\(\sqrt[3]{54}\)
\(\sqrt[3]{27 \cdot 2}\)
\(\sqrt[3]{27} \cdot \sqrt[3]{2}\)
\(3\sqrt[3]{2}\)
We Do
\(\sqrt[3]{16}\)
\(\sqrt[3]{8 \cdot 2}\)
\(\sqrt[3]{8} \cdot \sqrt[3]{2}\)
\(2\sqrt[3]{2}\)
You Do
\(\sqrt[3]{250}\)
\(\sqrt[3]{125 \cdot 2}\)
\(\sqrt[3]{125} \cdot \sqrt[3]{2}\)
\(5\sqrt[3]{2}\)
I Do: \(\sqrt[3]{54}\) = 3\(\sqrt[3]{2}\)
We Do: \(\sqrt[3]{16}\) =
You Do: \(\sqrt[3]{250}\) =
Independent Practice
\(\sqrt{20}\)
\(2\sqrt{5}\)
\(\sqrt[3]{40}\)
\(2\sqrt[3]{5}\)
\(\sqrt{180}\)
\(6\sqrt{5}\)
\(5\sqrt{24}\)
\(10\sqrt{6}\)
Exit Ticket
Simplify the following expression:
\(\sqrt{125}\)
Answer: \(5\sqrt{5}\)
Day 1 Summary
- To simplify a square root, find the largest perfect square factor.
- To simplify a cube root, find the largest perfect cube factor.
- Use the property \(\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b}\) to split the radical.
- Simplify the "perfect" part and leave the "leftover" part inside the radical.