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Square roots: exact and estimated
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Learn it To estimate $\sqrt{x}$, find the perfect squares on either side, then see how far x is between them.
Example: Estimate $\sqrt{55}$ to one decimal place.
- $7^2 = 49$ and $8^2 = 64$, so $\sqrt{55}$ is between 7 and 8.
- 55 is 6 of the 15 steps from 49 to 64: about $7 + 0.4 = 7.4$.
- Check: $7.4^2 = 54.76$ ✓.
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