Speedy Square Roots: The Estimation Game

Struggling to find square roots quickly? What if you could estimate them accurately without a calculator?

Subject: number-theory • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

This trick allows you to quickly estimate the square root of a non-perfect square. 1. Find the nearest perfect squares *above* and *below* the number. 2. Estimate where your number falls *between* those perfect squares. 3. Express this as a decimal. Why it works: Because the square root function is continuous and increasing, numbers close together have square roots close together.

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