Simplify – math problem (square roots or surds)?
Question:
Somehow, my calculator calculates result: (√6 – √2) / 4 from √(2-√3) / 2I need to know how to do this.
Answer
Here is a proof of ‘why’ (√6 – √2) / 4 = √(2-√3) / 2.8 = 8
8 – 4√3 = 8 – 4√3 ( subtract 4√3 from both sides )
8 – 2√12 = 8 – 4√3 ( because 4√3 = 2 x 2√3 = 2 x √4 x √3 = 2 √(4 x 3) = 2√12)
6 – 2√12 + 2 = 4 ( 2 – √3 ) ( modifying LHS and RHS appropriately )
(√6)^2 -2(√6)(√2) + (√2)^2 = 4 ( 2 – √3 ) ( Rewriting LHS equivalently )
(√6 – √2)^2 = 4 ( 2 – √3 ) ( using the identity a^2 – 2ab + b^2 = ( a – b )^2 with a =√6 and b = √2 ).
(√6 – √2) = 2 √( 2 – √3 ) ( Taking square roots both sides )
(√6 – √2) / 2 = √(2-√3) ( Dividing by 2 both sides )
(√6 – √2) / 4 = √(2-√3) / 2 ( Dividing by 2 again both sides )
QED.
