Choose an easy benchmark
An estimate uses nearby numbers to make a calculation easier. The sign ≈ means approximately equal; it does not mean exactly equal.
For 49 × 21, try 50 × 20 = 1000. One number goes up and the other goes down, but the changes do not necessarily cancel.
Nearby dimensions, not identical areas.
Check the original value
The original product is 49 × 21 = 49 × 20 + 49 = 980 + 49 = 1029.
Among 800, 1000, 1200 and 1400, the closest option is 1000. Its distance from 1029 is 29. The benchmark helped locate the answer without pretending that 1000 was exact.
Try a nearby square
Which option is closest to √2510: 50 or 60? Use nearby perfect squares.
2500 = 50² and 2601 = 51². Locate 2510 between those squares, then compare the possible square roots.
50² = 2500
2500 < 2510 < 2601
51² = 2601
Try it
Which option is closest to √2510?
- 50
- 60
Show the answer
50
50. Since 2500 < 2510 < 2601, the root lies between 50 and 51. It is less than 1 from 50, but more than 9 from 60.
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