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
√483≈22
- Find the perfect squares on either side. 441 is 21² and 484 is 22², and 483 sits between them.
- So the root is between those two whole numbers: √483 is between 21 and 22.
- 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.
- 01
Find the perfect squares on either side. 441 is 21² and 484 is 22², and 483 sits between them.
- 02
So the root is between those two whole numbers: √483 is between 21 and 22.
- 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.