Square roots to one decimal place, step by step

Once a root is bracketed between two whole numbers, the next question is which it is closer to.

The question

√483

21²=441
22²=484
441<483 < 484
√483is between21 and 22
21.9²=479.61
22²=484
22.1²=488.41
√48322
  1. Find the perfect squares on either side. 441 is 21² and 484 is 22², and 483 sits between them.
  2. So the root is between those two whole numbers: √483 is between 21 and 22.
  3. Now try tenths. 22² = 484, and the neighbors are 21.9² = 479.61 and 22.1² = 488.41. 483 is closest to 484, so √483 ≈ 22.

How it works.

  1. 01

    Find the perfect squares on either side. 441 is 21² and 484 is 22², and 483 sits between them.

  2. 02

    So the root is between those two whole numbers: √483 is between 21 and 22.

  3. 03

    Now try tenths. 22² = 484, and the neighbors are 21.9² = 479.61 and 22.1² = 488.41. 483 is closest to 484, so √483 ≈ 22.