2 − 6 4 = − 2 − 3 2 {\displaystyle {\frac ((\sqrt {2))-{\sqrt {6))}{4))={\frac {-{\sqrt {2-{\sqrt {3))))}{2))}
Multiplying by two:
2 − 6 2 = − 2 − 3 {\displaystyle {\frac ((\sqrt {2))-{\sqrt {6))}{2))=-{\sqrt {2-{\sqrt {3))))}
Squaring both sides:
2 − 2 ( 2 6 ) + 6 2 2 = 2 − 3 {\displaystyle {\frac {2-2({\sqrt {2)){\sqrt {6)))+6}{2^{2))}=2-{\sqrt {3))}
Simplified:
8 − 2 12 4 = 2 − 3 {\displaystyle {\frac {8-2{\sqrt {12))}{4))=2-{\sqrt {3))}
Multiplying by four:
8 − 2 12 = 8 − 4 3 {\displaystyle 8-2{\sqrt {12))=8-4{\sqrt {3))}
Subtracting eight and multiplying by negative one:
2 12 = 4 3 {\displaystyle 2{\sqrt {12))=4{\sqrt {3))}
Factoring a two from the right side and representing as the square root of four:
2 12 = 2 4 3 {\displaystyle 2{\sqrt {12))=2{\sqrt {4)){\sqrt {3))}
2 12 = 2 12 {\displaystyle 2{\sqrt {12))=2{\sqrt {12))}