What is √−√3+√3+8√7+4√3?

1 Answer
YouDid · Trevor Ryan. · Sidharth
Jan 5, 2015

If one may use a calculator, its 2
If no calculator is allowed, then one would have to play around with the laws of surds and use algebraic manipulation to simplify it.

Goes this way:

√7+4√3=√4+2⋅2√3+3=√22+2⋅2√3+√32=√(2+√3)2=2+√3 { This is using the identity(a+b)2=a2+b2+2ab}

√3+8√7+4√3=√3+8⋅(2+√3)=√3+16+8√3=√16+2⋅4√3+3=√(4+√3)2=4+√3{ This is using the identity(a+b)2=a2+b2+2ab}

√−√3+√3+8√7+4√3=√−√3+4+√3=√4=2

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