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If a^2+b^2+c^2=250 and a b+b c+c a=3, ...

If `a^2+b^2+c^2=250` and `a b+b c+c a=3,` find `a+b+c`

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Given:
`a^2+b^2+c^2=250`
`ab+bc+ca=3`
`(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)`
`(a+b+c)^2=250+2(3)`
`(a+b+c)^2=250+6`
`(a+b+c)^2=256`
`a+b+c=sqrt256`
`a+b+c=16`
`∴a+b+c=16`
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