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Answer 1 · 2017-03-17T13:02:07

$~~4.582$

To estimate you will need to d a lot of multiplication of squares by hand:

You know $sqrt(16) = 4$ and $sqrt(25) = 5$

This means the $sqrt(21)$ is in between. Since $21$ is about half way between $16$ and $25$ select the decimal $4.5$ and square it.

$4.5^2 = 20.25$ so we know we are getting close.

Try $4.55^2 = 20.7025$ which is smaller so we need a higher decimal value.

Try $4.57^2 = 20.8849$ which is smaller so we need a higher decimal value.

Try $4.58^2 = 20.9764$ Hope this is close enough. If not, try $4.582^2 = 20.994724$