Simplify: √48

Simplify radicals by finding perfect-square factors. Factor 48: 48 = 16 × 3, where 16 is a perfect square. So √48 = √(16 × 3) = √16 × √3 = 4√3. The perfect-square factor comes out of the radical; the remaining factor stays inside. Steps: (1) Find the largest perfect-square factor; (2) Rewrite as a product; (3) Apply √(ab) = √a × √b; (4) Simplify the perfect-square root. Perfect squares to recognize: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. Example: √72 = √(36 × 2) = 6√2. Example: √200 = √(100 × 2) = 10√2. If no perfect-square factor exists beyond 1, the radical is already simplified (like √7, √15, √23). Common error: stopping with non-largest factor — √48 = √(4 × 12) = 2√12, which is not fully simplified because 12 has a perfect-square factor of 4 itself.