Simplifying Radicals Math Example 3

Solution

1. 1
   Step 1: Factor inside the radical: $200 = 100 \times 2$; $x^4 = (x^2)^2$; $y^3 = y^2 \cdot y$.
2. 2
   Step 2: Rewrite: $\sqrt{200x^4y^3} = \sqrt{100 \cdot 2 \cdot (x^2)^2 \cdot y^2 \cdot y}$.
3. 3
   Step 3: Extract perfect squares: $10 \cdot x^2 \cdot y \cdot \sqrt{2y} = 10x^2y\sqrt{2y}$.
4. 4
   Check: $(10x^2y)^2 \cdot 2y = 100x^4y^2 \cdot 2y = 200x^4y^3$ ✓