Can You Simplify This Nested Radical Expression?
Автор: Math Hacks Hub
Загружено: 2026-01-30
Просмотров: 143
Описание:
Can you calculate √(1 + 3/√12) without a calculator?
Simplify: √(1 + 3/√12) = ?
This problem features a nested radical with a fraction inside! There's a brilliant simplification technique. The key is first simplifying √12 = 2√3, so 3/√12 = 3/(2√3). Rationalizing gives √3/2. Then √(1 + √3/2) = √((2 + √3)/2). Using denesting or recognizing this as a perfect form like √((√a + √b)/2), you can find the clean answer.
💡 Pause and try solving it before watching!
This problem teaches you:
✓ Nested radical simplification
✓ Rationalization techniques
✓ Denesting radical methods
✓ Fraction manipulation with surds
✓ Strategic simplification steps
Perfect for students preparing for:
• Math Olympiads (IMO, AMC, AIME)
• Competition mathematics
• Algebra II courses
• Anyone who loves radical simplification!
The answer is surprisingly clean once you simplify systematically!
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#matholympiad #mathematics #algebra #nestedradicals #rationalization #surds #denesting #simplification #problemsolving #mathchallenge #competitionmath #mathpuzzle #stem #algebraII
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