Question

using long division find the square root of 250.6404

Answer 1

Do a really rough estimate first using squares of multiples of
10
20
2
=
400
and
30
2
=
900
529
lies between
400
and
900
so
√
529
will lie between
20
and
30
Now look at the last digit ...
9

There are only two numbers whose squares end with a
9
,
3
and
7
→

3
2
=
9
and
7
2
=
49
So the possibilities are
23
and
27
However,
25
2
=
625
and
529
is less than
625
My first guess would therefore be
23
Multiplying confirms that
23
×
23
=
529
Hence
√
529
=
23