Question

2-2√2+√3-√5-√6+√10
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2+√3-√5

Answer 1

2-2√2+√3-√5-√6+√10 / 2+√3-√5 =
 =  (2-2√2+√3-√5-√6+√10)*(2+√3+√5) / 2+4√3 =
 = 4+2√3-4√2-2√6-2√10+2√3+3+√15-2√5-√15-5-2√6-√18-√30+2√10+√30+√50 /2+4√3 =
 = 4+2√3-4√2-2√6+2√3+3-5-2√6-3√2+5√2 / 2+4√3 =
=  2+4√3-2√2-4√6 / 2+4√3 =
= (2+4√3-2√2-4√6)(2-4√3) / -44 = 
= 2(1+2√3-√2-2√6)*2(1-2√3) /-44 =
=  (1+2√3-√2-2√6)*(1-2√3) / -11 =
= 1-2√3+2√3-12-√2+2√6-2√6+4√18 / -11 =
= 1-12-√2+12√2 / -11 =
= -11+11√2 / -11 =
= 11(-1+√2 ) / -11 =
= -(-1+√2 ) = 1-√2