Estimating square roots, step by step
√10 does not come out — so how big is it?
The question
√431
20²=400
21²=441
400<431 < 441
√431is between20 and 21
20.5²=420.25
431>420.25
√431≈21
- Find the perfect squares on either side. 400 is 20² and 441 is 21², and 431 sits between them.
- So the root is between those two whole numbers: √431 is between 20 and 21.
- Which end is it nearer? Halfway between 20 and 21 is 20.5, and 20.5² is 420.25. 431 is above that, so the root is nearer 21.
How it works.
- 01
Find the perfect squares on either side. 400 is 20² and 441 is 21², and 431 sits between them.
- 02
So the root is between those two whole numbers: √431 is between 20 and 21.
- 03
Which end is it nearer? Halfway between 20 and 21 is 20.5, and 20.5² is 420.25. 431 is above that, so the root is nearer 21.