Answer
10.247
Work Step by Step
$\sqrt {105}\approx10$
Divide and average to refine the approximation.
$105\div10=10.5$
$(10+10.5)\div2=10.25$
Repeat to further refine.
$105\div10.25=10.244$
$(10.25+10.244)\div2=10.247$
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