Estimate with useful benchmarks

Use easy nearby numbers, then check which option is closest to the original value.

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.

Original: 49 × 21
Benchmark: 50 × 20 = 1000

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.

8001,0001,2001,4001,029
1029 is 29 away from 1000.

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.

Use the squares to bound the root.

Try it

Which option is closest to √2510?

  1. 50
  2. 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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