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INTERMEDIATEApproximation
Estimate Square Roots
Quickly estimate square roots of non-perfect squares
SSCCAT
Find the two perfect squares the number falls between
Formula
√N ≈ a + (N - a²)/(2a + 1), where a² < N < (a+1)²How It Works
0
Find nearest perfect squares below and above
1
Calculate how far the number is from the lower square
2
Divide by difference between the two perfect squares
Examples
📝 √50: Between 49(7²) and 64(8²). 50-49=1, diff=15. √50 ≈ 7 + 1/15 ≈ 7.07
📝 √75: Between 64(8²) and 81(9²). 75-64=11, diff=17. √75 ≈ 8 + 11/17 ≈ 8.65
Pro Tips
💡 For quick estimates: if number is closer to lower square, answer is closer to lower root
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