Simplifying a Square Root

Simplifying a square root means factoring the largest perfect square out of the radicand and writing its root outside the radical.

Simplify √300. Factor for perfect squares: 300 = 100 · 3, and 100 is the largest perfect square inside. The product rule splits the root: √300 = √100 · √3 = 10√3. Check by squaring back: (10√3)² = 100 · 3 = 300. If the first factoring misses the largest square — say 300 = 4 · 75 — the method still lands: √300 = 2√75, and √75 = √25 · √3 = 5√3, so 2 · 5√3 = 10√3. Smaller squares cost extra passes, never correctness. The check step — squaring the answer back — catches most slips before they ship.