Answer
$2$
Work Step by Step
To get rid of radicals in the denominator, multiply both numerator and denominator by the conjugate of the denominator:
$\dfrac{\sqrt {2} + \sqrt {6}}{\sqrt {1.5} + \sqrt {0.5}} \cdot \dfrac{\sqrt {1.5} - \sqrt {0.5}}{\sqrt {1.5} - \sqrt {0.5}}$
Use the FOIL method to expand the numerator and denominator:
$\dfrac{(\sqrt {2})(\sqrt {1.5}) - (\sqrt {2})(\sqrt {0.5}) + (\sqrt {6})(\sqrt {1.5}) - (\sqrt {6})(\sqrt {0.5})}{(\sqrt {1.5})(\sqrt {1.5}) - (\sqrt {1.5})(\sqrt {0.5}) + (\sqrt {0.5})(\sqrt {1.5}) - (\sqrt {0.5})(\sqrt {0.5})}$
Multiply to simplify:
$\dfrac{(\sqrt {3}) - (\sqrt {1}) + (\sqrt {9}) - (\sqrt {3})}{(\sqrt {2.25}) - (\sqrt {0.75}) + (\sqrt {0.75}) - (\sqrt {0.25})}$
Simplify radicals:
$\dfrac{-1 + 3}{1.5 - 0.5}$
Combine like terms:
$\dfrac{2}{1}=2$
