Visual Approximation of Square Roots Visualization |Animation | Interactive applet GeoGebra #geogebra #math #science #iteachmath #mtbos #visualization #elearning Bernat ANCOCHEA #physics

Try my technique, it's a lot of fun. Babylonia🤝 Evdilla √3 = ? A) Let x · y = 3. B) Find a good approximation for this number. √1 < √3 < √4 Try x = 1.5. From x · y = 3, we find y = 2. C) H.M < G.M < A.M (2 · x · y) / (x + y) < √x · y < (x + y) / 2 (2 · 1.5 · 2) / (1.5 + 2) < √3 < (1.5 + 2) / 2 12 / 7 < √3 < 7 / 4 1.71 < √3 < 1.75 Therefore, √3 = 1.7... If you want more precision, apply a similar logic: C) Repeat part B. Use the confirmed digits as x. If x₂ = 1.7, then y₂ = 1.76 (2 · x · y) / (x + y) < √x · y < (x + y) / 2 (2 · 1.7 · 1.76) / (1.7 + 1.76) < √3 < (1.7 + 1.76) / 2 1,72 < √x · y < 1,73 √3 = 1,73... If you want more precision, apply a similar logic: D) Repeat part B. Use the confirmed digits as x. If x₃ = 1,73, then y₃ = 1,7341 (2 · x · y) / (x + y) < √x · y < (x + y) / 2 (2 · 1,73 · 1,7341) / (1,73 + 1,7341) < √3 < (1,73 + 1,7341) / 2 1,73204 < √x · y < 1,73205 √3 = 1,7320...

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