Multiply top and bottom by the conjugate of the denominator. √2 in the bottom becomes a whole number downstairs. 1/√2 × √2/√2 = √2 / 2. Exponent and root rules are in exponent rules.
Match the ugly piece
a + √b downstairs wants a − √b upstairs and downstairs. Complex conjugates are the same move for i, in complex conjugates. Union and intersection are a different leftover, in union and intersection.
The bottom line
Multiply by the conjugate. The denominator should come out rational.
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