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}}}
