Example

Estimating 60\sqrt{60} Between Two Consecutive Whole Numbers

Estimate which two consecutive whole numbers 60\sqrt{60} lies between.

Step 1 — Identify nearby perfect squares. List the perfect squares closest to 60 along with their square roots:

Number36496481
Square root6789

Step 2 — Locate 60 between two consecutive perfect squares. Since 49<60<6449 < 60 < 64, the number 60 falls between the consecutive perfect squares 49 and 64.

Step 3 — State the estimate. Because 49=7\sqrt{49} = 7 and 64=8\sqrt{64} = 8, the square root of 60 must lie between 7 and 8:

7<60<87 < \sqrt{60} < 8

The key step is building a short reference table of perfect squares near the target number so that the two bounding values can be identified quickly.

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Updated 2026-06-26

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