Square roots between integers, step by step

√10 does not come out even, but it is easy to place: it sits between 3 and 4.

The question

√446

21²=441
22²=484
441<446 < 484
√446is between21 and 22
√446>21
  1. Find the perfect squares on either side. 441 is 21² and 484 is 22², and 446 sits between them.
  2. So the root is between those two whole numbers: √446 is between 21 and 22.
  3. The smaller of the two is 21.

How it works.

  1. 01

    Find the perfect squares on either side. 441 is 21² and 484 is 22², and 446 sits between them.

  2. 02

    So the root is between those two whole numbers: √446 is between 21 and 22.

  3. 03

    The smaller of the two is 21.