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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 6060 along with their square roots:

Number3636494964648181
Square root66778899

Step 2 — Locate 6060 between two consecutive perfect squares. Since 49<60<6449 < 60 < 64, the number 6060 falls between the consecutive perfect squares 4949 and 6464.

Step 3 — State the estimate. Because 49=7\sqrt{49} = 7 and 64=8\sqrt{64} = 8, the square root of 6060 must lie between 77 and 88:

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 2026-04-21

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