College Algebra / Unit 1 Alg 050 worked example, 60 to 90 seconds
Simplifying a Square Root
The idea
Simplifying a square root means factoring the largest perfect square out of the radicand and writing its root outside the radical.
In practice
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.
Where people slip
A radicand with no perfect-square factor larger than 1 is already simplified.
Your place on the trail
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Builds on
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Unlocks
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