Question 1068663
{{{D[1]^2=(4-0)^2+(2-0)^2}}}
{{{D[1]^2=16+4}}}
{{{D[1]^2=20}}}
{{{D[1]=4sqrt(5)}}}
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{{{D[2]^2=(4-10)^2+(2-0)^2}}}
{{{D[2]^2=(-6)^2+4}}}
{{{D[2]^2=36+4}}}
{{{D[2]^2=40}}}
{{{D[2]=2sqrt(10)}}}
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{{{D[3]^2=(4-3)^2+(2-5)^2}}}
{{{D[3]^2=1+9}}}
{{{D[3]^2=10}}}
{{{D[3]=sqrt(10)}}}
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So then,
{{{D[1]+D[2]+D[3]=4*sqrt(5)+2*sqrt(10)+sqrt(10)=m*sqrt(5)+n*sqrt(10)}}}
Now solve for m and n.
And then add them to get the final answer.

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By the way, the actual minimum occurs at ({{{3.34}}}, {{{2.64}}}).